what symbolically speaks as "the darkness of man's heart" is also, literally, the lord of the flies - the devil.

Hope it helps!

Firstly, let's talk about the symbols in this chapter.

Piggy is the symbol of civilised life and actions. He is overweight, ill with asthma (ass-mar as the boys call it) and has poor eyesight. He been able to overcome these shortcomings somewhat through the inventions of the modern world (symbolised through his glasses). Throughout the novel, it is Piggy who reminds the boys to remember their civilised, human selves, by insisting that they treat each other with respect by calling everyone by their name and by creating a structured and respectful way to discuss and solve problems through the use of the conch. Ironically, Piggy is one of the only boys who does not receive the same treatment he has demanded for the others. He remains "Piggy".

Piggy's glasses are a symbol of the innovation of the modern world - where problems can be overcome with intelligence and creativity. In this world, all people can be equal and the weak are protected. This is in stark contrast to the savagery of more primitive life - where violence and strength are used to overcome adversity and where weakness and soft-heartedness are scorned and can lead to death. Ralph's "camp" is robbed of the glasses by Jack, Roger and the others, so that they will be successful with fire in their new camp with the Lord of the Flies. Without the glasses, Ralph, Piggy and the boys are unable to maintain their signal fire, which is their hope of being rescued by adults.

The Conch is the symbol of a life of order and respect. It is used to gain the attention of the group, and as a turn-taking tool for group discussions. Both of these actions are part of an ordered, safe society. It is smashed by the boy least able to understand civilised ways - namely, Roger, who takes pleasure in hurting and destroying.

The Lord of the Flies (the pig's head) is a symbol of the savagery that the boys have found within themselves and created around them. It was discovered by Jack after the boys had slaughtered a sow suckling her young. The Lord of the Flies allows Jack to become a religious leader for the boys, in which role he makes them follow quasi religious rituals in honour of the Lord of the Flies. The Lord of the Flies is destroyed by Ralph, who is arguably the least savage amongst the leaders.

Piggy is killed by the boulder that Roger rolls down the side of the hill. In line with his non-athletic nature, Piggy is unable to escape the rock and is struck down, and rolls off the side of the mountain.

His body floats away from the savagery of the island to the peace of the sea. 

Simon, who is the one character who has discovered that the "Beast" is not a real being, but rather the evil that lurks within all of them. Simon is murdered by the boys who mistake him for the beast. His body is washed into the sea in a violent storm, symbolises an act of cleansing away the the goodness in Simon from the evils that have grown on the island.

For Ralph in Chapter 12 of "The Lord of the Flies," the pig's head represents the raw and rapacious savagery of Jack and the hunters.

He argued unconvincingly that they would let him alone, perhaps even make an oulaw of him.  But then the fatal unreasoning knowledge came to him again...These pained savages would go further anf further....A spasm of terror set him shaking and he cried aloud.....The skull [of the pig] regarded Ralph like one who knows all the answers and won't tell.

Ralph realizes that this act of posting a lifeless--or was it?--skull of a pig on a post represents the end of civilization in the hunters.  As a result, he feels

his isolation bitterly....Lying there is the darkness, he knew he was an outcast. 

Ralph also realizes that rationality has left the group led by Jack and he must try to survive their hunt of him:

He forgot his wounds, his hunger and thirst, and became fear, hopeless fear on flying feet....

As he stumbles over a root, he sees the shelter butst into flames ; then, he is down, rolling over and over in the sand, "crouching with arm to ward off, trying to cry for mercy' until the deus ex machina arrives in the form of a naval officer who has seen the flames and has come to rescue them.

The boys' descent into evil as they follow Jack is sealed when they sadistically and ritualistically slaughter a pig and eat it, enjoying both the pleasure of triumph over the helpless creature and the pleasure of eating the dripping meat.

Simon, the Christ figure in the novel who represents the superego or conscience, hallucinates as he looks at the dead pig's head, which has been mounted on a stick as if it is an idol to worship. It is surrounded by flies, bringing to mind Beelzebub, the devilish second-in-command to Satan in Milton's Paradise Lost. Milton conceived of the demons in hell in traditional terms as like a swarm of flies.

Simon has spiritual insight into the true meaning of the pig's head as a symbol of evil. This insight emerges in his conversation with it. It says to him,

Fancy thinking the Beast was something you could hunt and kill!

This makes explicit that evil—the "Beast" the boys fear—is within their souls rather something external that can be hunted down and destroyed.

Second, looking at this symbol of evil helps Simon to understand how powerful its allure is. What he, Simon, represents, the head says is not wanted. The boys, led by evil impulses, desire what the head calls "fun": the opportunity to run wild and indulge all their normally forbidden, atavistic instincts towards violence, domination, and cruelty. The boys also wish to live irresponsibly in the moment.

Simon can see through to the core of what this "fun" really is—a rotting, dead head surrounded by flies, something disgusting—but the other boys see only the outer shell of what appears to be freeing and deeply enjoyable. The head says,

You’re not wanted. Understand? We are going to have fun on this island.

The head, the symbol of evil, lies, just as the devil does, because what the boys are having will not turn out to be fun, but a destructive fire that threatens to consume them.

In chapter eight of Lord of the Flies, by William Golding, Jack and his hunters sharpen a stick at both ends and place the dismembered, bloody head of a pig on it. Jack knows his hunters, like nearly all the boys on the island, have a fear of some nameless beast; he hopes to allay some of those fears by this act. He tells his hunters that they are leaving a sacrifice to appease the beast, though the reality is that the creature Simon sees as Lord of the Flies is really just a pig's head jammed onto a stick. Symbolically, the pig's head is much more than that.

Simon has a hiding place where he goes to be away from everyone, and he is there when the hunters erect the faux sacrifice right outside of his secret hideaway. We know that Simon has a tendency to faint, and through the course of his conversation with the Lord of the Flies we have indications that this dialogue is not real but conducted in Simon's head. At the end of the conversation Simon faints.

The Lord of the Flies tries to intimidate and threaten Simon; he calls Simon "just an ignorant, silly little boy" and mocks Simon for thinking the beast is "something you could hunt and kill!" Golding uses this symbolic beast, the Lord of the Flies, to reveal the truth to Simon: they, the boys, are the beast. The Lord of the Flies says,

“You knew, didn’t you? I’m part of you? Close, close, close! I’m the reason why it’s no go? Why things are what they are?”

Before Simon faints, the Lord of the Flies warns Simon that he is not wanted on this island (because Simon represents the soul and spirit of man) and predicts that "Jack and Roger and Maurice and Robert and Bill and Piggy and Ralph" will kill him. And they do.

Piggy, who has always appeared older than the other boys with his thick body and thinning hair and poor eyesight, is representative of maturity of thought and rationality. For he is the one who finds the conch and suggests to Ralph that it can be used for assembling the boys; he is the one who suggests that the boys with him can make a fire on the beach as a signal just as easily as on the mountain after Jack and the hunters steal the fire. 

But Piggy's maturity and rational behavior is threatened by the savagery of the hunters who steal his glasses, and the sadism of Roger. So, in Chapter Eleven when Ralph and Piggy and the others approach the hunters to demand the return of Piggy's glasses, Roger arrests their approach. Ralph identifies himself and says that he is calling a meeting, but Roger keeps his hand upon the lever of the rock that is poised over the bridge. After Jack usurps power from Ralph, Roger releases the boulder with "delirious abandonment" and it strikes Piggy, hurling him downward to death, symbolizing the end of all rationality and civilized behavior.

His head opened...and turned red. Piggy's arms and legs twitched a bit....Then the sea breathed again in a long, slow sigh...sucking back again, the body of Piggy was gone.

As heart-breaking as Piggy's violent death is in Lord of the Flies, Golding uses the moment symbolically to represent an end to civilization and order on the island.  Roger, the symbol of ultimate evil, releases the giant boulder that smashes the conch and kills Piggy; his death is incredibly symbolic, especially in the way he dies; being smashed by a boulder is not only an extremely violent way to die, but it is also senseless and meaningless.  The moment is a snapshot for the most important theme of the novel, civilization and order against chaos and savagery. 

Piggy's death is extremely similar to Simon's in that both result from violent savagery under Jack's guidance and leadership.  Although Piggy's death had a much different setting, Roger is the instigator; his action of leaning on the lever resulted in the boulder crushing Piggy.  Roger also figures as one of the key instigators in Simon's mob-death, because Roger takes up the role of play-acting inside the circle before Simon enters in the dark and is killed by the boys. 

In both murder scenes, the killing of each boy stems from a 'mob mentality,' whether it is the deathly dance circle which pulverizes Simon or the 'us versus them' mentality that lends Roger the confidence to lean on the lever under the boulder.  If Roger had felt in any way insecure in his position, he would not have been gutsy enough to kill Piggy; but at Castle Rock, surrounded by other savages and Jack as the wild chief, Roger felt just the right amount of security that he needed to know that his foul deed would be accepted, even embraced.

Similarly, the aftermath of both deaths takes place in the sea, where the waves wash away the evidence of the boys' wrong doing.  Simon's body travels out to sea, and Piggy's body is knocked over the side of the cliff and onto the rocks.  Golding uses the sea as a cleansing agent in the novel, erasing the record of the boys' murderous deeds, therefore making them more easily forgotten or ignored. 

Both Simon and Piggy's deaths are the culmination of unchecked savagery and violence.

Pigs do come into play in the symbolism of Golding's novel Lord of the Flies; however, they are not a straightforward symbol in that they are used to represent a variety of different ideas. The sow and her nursing piglets represent the innocence of nature; hunting pigs represents the baser human desires; and the "pig's head on a stick" represents the depravity of the human heart. In chapter 8, Jack leads the boys on a pig hunt, and they find several pigs contentedly sleeping in the shadows. Among them is a sow nursing a row of piglets, "sunk deep in maternal bliss." The boys wound her and chase her, trailing her blood, until she comes out into "an open space where bright flowers grew and butterflies danced round each other." As the boys fall upon her, "this dreadful eruption from an unknown world made her frantic." She is brutally killed as the butterflies continue to dance. Golding's description of the blissful pig, tormented and killed by an invading species, speaks of the peaceful innocence of nature on the island apart from the corruption that man brings. 

The novel uses hunting extensively as a symbol of baser human instincts and desires. In the passage where the boys kill the sow, Golding describes how the boys were "wedded to her in lust," and after they kill her, they were "heavy and fulfilled upon her." The desire for hunting and meat causes the boys to leave the signal fire unattended just as a ship passes the island. Jack is able to lure the boys over to his tribe by the enticement of meat, even though most of the boys prefer Ralph as chief when they are thinking about rescue. 

When the boys have killed and gutted the sow, Jack mounts its head on a stick and leaves it as a gift for the beast. Simon, concealed in the thicket, ends up having a vision where he converses with the head. Golding calls the head the Lord of the Flies, and it identifies itself to Simon as the Beast. During the conversation Simon's previous understanding that the beast is "mankind's essential illness" is confirmed when the pig's head says, "You knew, didn't you? I'm part of you? Close, close, close! I'm the reason why it's no go? Why things are what they are?" In this way Golding presents his message that the downfall of the boys' society stems from the depravity in their hearts.

Pigs play a key role in the symbolism of Lord of the Flies and are used at various points to symbolize the innocence of nature, the baser human desires, and human depravity.

Simon comes across the pig's head in chapter 8. Previously Simon went to that clearing area and was amazed at the beauty of it all. That clearing was a place of peace and harmony to Simon, a place where things made sense to him and a way to escape the craziness that was beginning to take hold of some of the boys, like Jack.

When Simon returns to his quiet place in chapter 8, he sees the head of the sow on a stake. It represents a complete abomination to Simon. It is the complete destruction and desecration of the clearing. While Simon is staring at the pig's head, he begins hearing a voice: the voice of the Lord of the Flies. But to Simon it sounds as if it is coming from his own mind, which is a deep revelation to Simon. The beast that all of the boys fear is not an actual beast, but the potential for evil that lurks in the hearts and minds of each person. The boys need not fear any actual beast on the island, but need to fear each other.

The pig's head represents the realization that each of the boys can be their own worst enemy.

Piggy is a social outcast. He has asthma, which he calls "ass-mar," wears glasses, and is fat. He tells Ralph that at school he used to be called Piggy, which is what he is called on the island. So already, we are associating this character with the animal he is named for.

In chapter four, Jack and his hunters kill a pig for food. Their hunting turns to savagery when they take down a pregnant sow. At this point they are bloodthirsty, as evidenced by their chants and the multiple stabbings they carry out . It might have been smarter to hunt another pig for the sake of sustainability and let the sow give birth to more pigs that could be hunted for food.

In their mania, the boys kill Simon while chanting "kill the beast!" Simon crawled toward them at night during a storm. There is no chance for confusion with Piggy's death, however. Roger pushes a boulder on top of him. Piggy has "no time for even a grunt," and his "arms and legs twitched a bit, like a pig's after it has been killed."

Piggy's murder shows the departure from civilization. He is equated to an animal because the boys kill him like they would an animal. They have lost their humanity.

For one thing, his name connects him.  Piggy, Ralph, and Simon never fit into Jack's group.  They were the reasoners, the order and peace keepers, the ones who made everyone understand the seriousness of the situation and the importance of everyone doing his amount of work in order to survive.  This did not fit into Jack's plan of having fun and hunting for food. 

So, the three of them were "hunted" just as the wild pigs on the island. Simon succumbed early to stabs on the beach, and Piggy followed not long after with a boulder to his head.  Only Ralph survived the hunt, but probably would not have had the Navy not spotted the island-wide fire Jack set to "smoke" the piggy Ralph out of his hiding place.

Early in his novel, William Golding introduces the motif of stones and rocks. In Chapter One, for instance, as the boys discover the island, the perceive

a great platform of pink granite thrust up uncompromisingly through forest and terrace and sand and lagoon....

In fact, the pink granite is on several cliffs. On one summit, the boys heave the rocks until they smash a hole in the canopy of the forest.  This act foreshadows the toppling of the huge rock that kills Piggy. Then, in Chapter Four, Golding as narrator alludes to the stone, "that token of preposterous time" that the sadistic Roger throws around little Henry who plays in the lagoon. At this time, he does not hit Henry because his arm has been conditioned by a civilization "that knew nothing of him and was in ruins."

But, once Roger is liberated from this "shame and self-consciousness" by the savage mask of face paint that Jack creates along with the hunt, he becomes impervious to any rules of conduct and frees his darker side. After one hunt, Roger plays the pig, grunting and charging at Jack. And, as the hunters descend more and more into savagery, Roger becomes more and more sadistic until he begins to terrorize Sam'n'Eric by flinging a stone between them:

They parted and Sam only just kept his footing.        Some source of power began to pulse in Roger's body. 

As the boys descend into savagery, there are fewer and fewer of the boys are on the side of Ralph and Piggy. Aggression begins from Roger's side.  In Chapter Eleven, Roger is at the top of the mountain: 

High overhead, Roger, with a sense of delirious abandonment, leaned all his weight on the lever....He was aware of a jolt in the earth that came to him through the soles of his feet...He obeyed an instinct that he did not know he possessed ....

and Piggy's body is hurled into the ocean.  After the boys' yelling ceases, Roger "advances upon them as one wielding a nameless authority," the authority of savage power represented by the large pink granite boulder. 

As pointed out by the first answer to your question, the Lord of the Flies is a pig's head on a stick, but Golding manipulates its literal portrayal--a dead pig's head on a stick surrounded by flies--to create a very figurative meaning for the reader.  The image itself represents death and decay, a waste of life, so Golding uses that image to create a much deeper meaning in the text, using the dead pig's head as a front for the metaphorical Lord of the Flies. 

"[The flies] were black and iridescent green and without number; and in front of Simon, the Lord of the Flies hung on his stick and grinned.  At last Simon gave up and looked back; saw the white teeth and dim eyes, the blood--and his gaze was held back by that ancient, inescapable recognition" (138).

Golding's use of detail, from the color of the flies to the sharp contrast of the "white teeth and dim eyes," creates a horrible picture of destruction; his use of the name 'Lord of the Flies' alludes to Beezelbub, a name literally meaning 'Lord of the Flies,' taken from the Old Testament of the Bible for the devil, representing that deeper sense of evil, what Simon perceives with "ancient, inescapable recognition" (138).  Simon's encounter with the Lord of the Flies is made all the more disturbing and grim through Golding's use detail and imagery.

Piggy is very much the voice of reason. A highly intelligent boy full of common sense and good ideas, he shows the best way forward for the boys to survive and thrive on the island. Unfortunately, hardly anyone listens to Piggy. To most of the other boys, he's just a figure of fun, an overweight, short-sighted outcast who deserves to be treated with contempt.

But as long as Piggy's around, he can't be completely ignored. He will always act as a reminder that there is a much better way of doing things. And most of the boys don't want to be reminded of that. They just want to have fun and do as they please: to hunt pigs and generally treat the island like a gigantic playground, an opportunity for adventure. To them, Piggy is not just a source of irritation and contempt; he is a spoilsport, putting a dampener on their enjoyment.

When the psychotic Roger kills Piggy, there is a tragic sense of inevitability about it. The reason that Piggy represents simply cannot be expected to survive for very long in the midst of such utter savagery. When Piggy was alive, there was always a chance—albeit somewhat remote, it should be pointed out—that reason could eventually prevail over the forces of barbarism. But once Piggy is killed by Roger, all such hopes are completely lost, and the final descent into total barbarism begins with a vengeance.

The acts of murder that occur in the story are a way of showing the breakdown of social order. The boys, away from the strict rules and structures of their school, are shown to be capable of violence, cruelty, and tyranny. Because Jack's "tribe" rebels against Simon and Piggy, the de facto "leaders" due to their intelligence and desire to maintain order, it can be seen as a rebellion against the same sort of social order and leadership they had back home before their exile on the island. "Pig" is a slang term for law enforcement and it is possible that the slaughter of Piggy is symbolic in this way: a killing and destruction of social order, authority and rules of law (such as the use of the conch for speaking).

The pigs of the island are also a sort of authority presence, since they have lived there for a long time and know the environment; they have a sort of expertise and wisdom regarding this place that the boys do not. The pigs are like an elder indigenous tribe of the island, knowledgable of its traditions, and in that way deserving of respect. By killing the pigs recklessly, especially the mother pig who could have helped provide a more sustainable food source, the boys are literally murdering wisdom and tradition. Piggy's murder is similar: by killing him for wanting to exercise a traditional sort of leadership and logic, Jack and his followers are overthrowing the old rules in favor of a sort of anarchy based in selfish needs instead of logic, order and cooperation.

The first pig was killed to provide meat, but then the killing became more of a power trip for Jack and his tribe.  When they kill the mother pig, they are foolish because they are killing what could be a future source of food.  Rather than look for another pig, the killing is done because they CAN kill. It is senseless.  The killing of Piggy is senseless, too, for the most part.  Piggy represents intellect and killing him is therefore killing intellect on the island.  In the aspect that it was essential to kill intellect on the island so that the evil could fully emerge, then killing Piggy was essential just like killing the pig for food was essential.