The unsettling, disturbing, and "gaunt" figure that enters Prince Prospero's bizarre masquerade is the personification of the deadly pestilence and symbolically represents death. Prince Prospero and his wealthy friends barricaded themselves inside his castellated abbey to avoid the devastating plague and believed that they could outwit death. Despite their arrogance and bold attempt to survive the disease, the Red Death enters the ball in human form at the stroke of midnight.

When the personification of the Red Death enters the imperial suite, the prince and his guests are frozen in fear and stare at the ghastly figure, who "out-Heroded Herod." The uninvited guest resembles the Red Death by wearing "habiliments of the grave," moving like a "stiffened corpse," and having awful blood splatters on its face. The appearance of the Red Death is a disturbing warning to the haughty guests that their attempt to outwit death has failed.

In addition to looking like a "stiffened corpse," the horrifying "spectral image" also arrives at midnight and travels to the seventh chamber, which is further evidence that the masked figure symbolizes death. In the story, each stroke of the hour reminds the guests of their own mortality, and midnight symbolically represents the end of their lives. Since the imperial suite is arranged to reflect the course of one's life, the seventh, most western chamber is also associated with death. It is in the seventh chamber where Prince Prospero and his guests die at the feet of the personification of the Red Death, which held "illimitable dominion over all." Overall, the masked figure represents the deadly pestilence and symbolizes death.

It's notable that Prince Prospero's guests are absolutely terrified of the “tall” and “gaunt” figure “shrouded from head to foot in the habiliments of the grave.” For in this ghoulish specter, they see death—their own deaths, to be precise. The masked figure, with his mask that looks like the face of a “stiffened corpse,” is the perfect representation of death, which comes to all of us at some point.

But Prospero's guests don't want to be reminded of this. They've descended upon their host's castellated abbey precisely in order to avoid the plague that rages outside, which has brought so much suffering and death to so many. They came here to escape the plague and enjoy themselves. The last thing they want is to be reminded of their own mortality.

But the truth, of course, is that they cannot avoid death; no one can. Whether they choose to avoid it, run away from it, or even embrace it, it makes no difference whatsoever. No matter how safe they might think they are locked up behind the walls of Prince Prospero's stately pile, they will never be able to escape the cold, clammy hand of death upon their shoulders.

In one sense, the masked figure who crashes Prince Prospero's party is representative of the disease -- called the Red Death -- that ravages the kingdom.  The disease is referred to as the Red Death because it is characterized by the hideous quantities of blood that seem to pour out of a person when they have contracted it.  The narrator says of the disease, "Blood was its Avatar and its seal -- the redness and the horror of blood" because its victims would literally bleed from all their pores before they died.  The masked figure comes, having "assume[d] the type of the Red Death."  His clothes are "dabbled in blood -- and his broad brow, with all the features of the face, was besprinkled with the scarlet horror."  He is the disease, personified.

However, the masked figure is more than just the disease.  He can be interpreted as a symbol of death, in general, too.  His mask looks like the face of "a stiffened corpse," and he is first seen by Prince Prospero as he stalks through the seventh room of black and red.  This is the only room to be characterized by two colors, and so they both must be significant.  Just as red is associated here, with the fatal disease, so black is often symbolic of death in general.  Likewise, clocks are often symbolic of mortality and death, and so the ebony clock in this room provides another clue that anything associated with the room is likewise connected to death.  It is not the Red Death, the disease, that holds "illimitable dominion over all" but rather death in general.  No human, no matter their status, can escape death, though the prince clearly thought that he could.  Thus, the masked figure represents both the bloody disease as well as death, generally speaking.

It has a threefold meaning:

First, it represents the red death itself, infiltrating itself in the castle with no idea from the courtiers.

With this, another meaning is ascribed:

First, the inevitability of Fate- No matter how much they ran, they still were followed by the red death.

Second, the vulnerability of man- Again, as much as they tried to control a situation by sheltering themselves, it went and found them.

Third: Fate itself- The courtiers tempted it, and she got them- The illness appeared in the castle, as guarded and as sheltered from it as it was.

The figure you refer to in Poe's "The Masque of the Red Death" is death.  There's no hiding from death, and it gets us all sooner or later.

The speaker describes the figure:

The figure was tall and gaunt, and shrouded from head to foot in the habiliments of the grave.  The mask which concealed the visage was made so nearly to resemble the countenance of a stiffened corpse that the closest scrutiny must have had difficulty in detecting the cheat. 

Habiliments are garments used to wrap corpses, and visage is the figure's face.  In addition, the figure is splattered with blood, its brow "besprinkled with the scarlet horror." 

The figure cannot be kept out no matter what is done to stop it, and in the end it kills everyone.  The figure represents death. 

Many would say that the masked guest who looks like death represents death itself. For example, the guests are afraid of the masked figure and they are also afraid of dying.  No one has the "guts" to unmask the man.  Also, no one can escape death; the guests attempted to "hole up" on Prince Prospero's mansion; however, they could not be protected from death because death finds all no matter race, ethnicity, age, religion, etc.:

The last line of the story indicates that the Red Death has triumphed over life: "And Darkness and Decay and the Red Death held illimitable dominion over all.’’ (eNotes)

What do the Masqueraders represent in "The Masque of the Red Death"?

In the story "The Masque of Red Death", the masqueraders are the people who were closest to Prince Prospero. They were the people who followed him and did as he wished, courtiers. That is precisely whom they represent, nobles and aristocrats.

The fact that they represent the upper class is very telling. When you think of the masks that they wear, oblivious and careless about the situation going on in the outside, it makes us think of everyone who has blindly followed a leader, or a cause, without really thinking about it. 

Notice how they obey every whim of Prince Prospero. They do not even get to pick their own costumes. If Prospero wants them to look beautiful, or disgusting, or frightening, it was not up to them; they had to submit to whatever their ruler asked. 

it was his own guiding taste which had given character to the masqueraders. Be sure they were grotesque.

Their attitudes are equally telling of what they represent. They characterize them as aloof individuals, and as people who are too preoccupied with the mundane and the superficial to care about what really needs to be taken care of. Like the first line reads, Prince Prospero's own tastes guided them. In fact, he guided them completely. Blindly, they followed. They did not care what was the outcome. They were too busy with the shallowness of it all. 

There were much glare and glitter and piquancy and phantasm--[...] There were arabesque figures with unsuited limbs and appointments. There were delirious fancies such as the madman fashions. There were much of the beautiful, much of the wanton, much of the _bizarre_, something of the terrible, and not a little of that which might have excited disgust.

Therefore, the masqueraders represent the calloused, unsympathetic upper class leaders of the world. They embody carelessness, shallowness, and an overall blindness of what really matters. 

What is the significance of the word "masque" in "The Masque of the Red Death"?

The word “masque” refers to the fact that Prospero and his guests are hiding, masking the reality of the situation.

Prince Prospero’s kingdom has been hit with a terrible plague—the Red Death.  In response, Prospero gathered his rich courtiers and they locked themselves away in the palace for constant partying. The fact that it was a masquerade just emphasized how out of touch they were with reality.

When the clock strikes 12, death arrives.

[There] were many individuals in the crowd who had found leisure to become aware of the presence of a masked figure which had arrested the attention of no single individual before.

The representation of death as a masked figure represents both the isolation of the partiers and the fact that no one knows what death looks like or expects it.  Prospero is irritated by the masque, which is designed to look like the Red Death.

His vesture was dabbled in blood—and his broad brow, with all the features of the face, was besprinkled with the scarlet horror.

Prospero considers it an insult because his “guest” is mimicking the very thing they are hiding away from.  Death is reminding him that he has abandoned his responsibility to his people.  It is a reminder to all leaders (and wealthy individuals), that with wealth comes responsibility.