of the human race. In their own ways, each is a heart of darkness.

Certainly Kurtz has lost his bearings as his way as an individual. Even the madness or insanity that some reader's see in him is merely a manifestation of his own downfall. He, himself, is a "horror."

Likewise, the misguided attempt to colonize and exploit Africa is also a "horror." Kurtz, perhaps unlike most of the other characters of the novel, sees just foolish and precarious such a proposition truly is. Africa has no use for and no reason to tolerate the invasion of the Europeans.

But, central to the entire work, is Conrad's comment on the essential nature of the human spirit--the idea that we all are corrupt and evil at the core and that we merely need the right conditions and triggers to bring those elements to the surface. The heart of darkness is both a physical place on the African continent and a spiritual place at the core of the human soul.

This is the subject of much in way of debate and discussion.  You will find many different interpretations of Kurtz's dying words.  Some believe that that last words indicate his own reflection of the life he has led.  "The horror" could indicate a summation of what colonization was on the lives of the indigenous people, and might be a discussion point of how colonization might have started off with noble intentions, but was highly corrupt in its practice.  Another read could be that Kurtz's own descent into madness revealed much in way of "the horror."  The words help to identify what lies at the center of a corroded soul.  In a larger sense, perhaps the meaning of the words is not a precise read, as much as an overall state of being in the world when one has lost a sense of clarity and vision to guide.  Perhaps, "the horror" is the realization that there is no such vision at all. The only absolute in this setting is human freedom, which could very well be "the horror."

The ambiguity of Kurtz's last words are meant to make readers reach their own conclusions about Kurtz's state of mind in his final lucid moment; we know this because Marlow has his own set of questions about what Kurtz is thinking at the end. Marlow looks at Kurtz and sees "somber pride," "ruthless power," "craven terror," as well as "intense and hopeless despair." If Marlow reads Kurtz's expressions correctly, the words "the horror, the horror" could be a recognition of what evil he has done in amassing his cache of ivory and consolidating his power over the natives; it could be awe and satisfaction at his own power, fear of the commencement of eternal punishment, or profound shame. Suffice to say that Kurtz does not die in a state of equanimity. Marlow believes that Kurtz sees a "vision" or "image" in his last moments and that it in some way provokes him.  

Later, as Marlow waits to speak with Kurtz's "intended," he recalls Kurtz's last words and imagines him "embracing, condemning, loathing all the universe." It seems clear that Marlow believes that Kurtz is a failed Satanic figure, capable of great evil, but in the end, vanquished by his own overreaching nature. 

Here is another possible interpretation. But again, it's important to bear in mind that there's very little in the way of academic consensus on this point, so it's a good idea to research as many opinions as you can.

As often happens when someone is close to death, Kurtz's whole life starts to flash before his eyes. He's always considered himself to be a good man, yet now his soul has been totally brutalized and corrupted by his experiences in Africa. But in his final words, he isn't simply articulating the horrors of what he's seen and done; he's alluding to the fundamental horror at the heart of all human existence. He's realized too late that, beneath the thin, tenuous veneer of civilization, we're all pretty much the same. In turning himself into a god, Kurtz has rejected God, arrogating to himself the power of life and death over others. Finally, he comes to realize the full horror of what this power entails, and stares into the dark, existential abyss that awaits us all.

These words are potently enigmatic. I like the ideas offered above and I'd offer another interpretation. The horror that Kurtz sees in his vision/realization is one of his failure (to truly move beyond humanity, to become more than human; a god or something not far short of that) and the horror is also a realization of the chaos that exists in "the beyond", a space where gods might dwell and live but which men cannot enter. 

Kurtz' goal was one of supremecy, extreme supremecy. He fails to become something more than he was at the beginning. He is bound to human morality and, like the first interpretation offered above, he finds in the end that he must judge himself according to the laws of society as he has failed to forge his own set of laws in the jungle. 

There are so many interpretations of this quotation!  Here are a few that I find most plausible.

By the end of his long stay at the inner station, Kurtz has realized that his treatment of the natives, his rebel attitude and actions toward the company and his own self-destruction are truly horrible and antithetical to the person he was before he entered the "heart of darkness."  Therefore, his outburst reveals this awarenes of what he has become.

Another interpretation is just about the opposite.  Being forced to leave his sanctuary, where he is treated like a god, and to return to a life that he no longer respects is overwhelming to Kurtz.  His final words are a reaction to this reality that he in no way wants.

Finally, many interpret Kurtz words as a reaction to a vision he has while he is near death.  He has perhaps caught a glimpse of hell and is realizing for the first time where he will spend eternity.

Of course other interpretations exist.  The best may be a combination of several ideas!

The dying words of Kurtz are some of the most renowned and enigmatic words in the history of Western literature. As a figure of epic ambitions and possible insanity, Kurtz stands as a mysterious and ambigious literary character, bent on greatness and willing to go further than any sane person would to achieve it. 

One way to read this novel is to see it as an exploration of moral limits. Kurtz is following the Nietzschean edict of the uber-man and attempting to go beyond the moral world of his peers to construct his own morality. 

Marlow recognizes Kurtz as a man in the midst of an epic existential stuggle: 

I saw the inconceivable mystery of a soul that knew no restraint, no faith, and no fear, yet struggling blindly with itself.

The struggle was to move beyond the order of the human world of morality, to break free of moral contraints and create a new set of laws. What Kurtz found, in the end, was that beyond the human world is only chaos. There is no "other order" and this is the nature of "the horror".

The horror is the chaos that Kurtz has entered, a world without morals and where no new laws can be formed, where he is powerless.  The horror is, also, his realization of his failure and his inability to be more than human. 

Another argument is made suggesting that Kurtz, in his ambition and his greed, had entered the heart of the wilderness and there became wild. He "regressed" to a point of savagery more fiercely untamed than any of the people in the book described as "savages". 

He pursued a line of self-inquiry in the depth of the jungle which brought him, alone and wild in his very soul, to the brink of animalism, a place from which he could not turn and upon which he could not prevail. Again, we have Kurtz involved in a supreme effort of will. He fails, absolutely, because he is not a god, as he wishes to be, nor an uber-man. He is merely a man. This is his "horror". 

Your question clearly points to four of the most well-known words in the English language when we think of literature! I think it is important to discuss what Marlow thinks of what Kurtz says and how he interpreted it. As the boat travels swiftly down the river, Kurtz's life is fast running out, and it seems that almost to the end he remains self-deceived. However, just before he dies, it is "as though a veil had been rent" and Marlow reads on his face contradictory emotions of pride and ruthless power on the one hand, but on the other hand, terror and hopeless despair. Kurtz's last moment is one of "complete knowledge" we are told, when he exclaims "The horror! The horror!" Marlow tells us that he interprets Kurtz's final words as "a judgement upon the adventures of his soul on this earth." Whatever the truth Kurtz has glimpsed, Marlow sees its perception as a "moral victory". In other words, he approves of Kurtz's achievement of consciousness; that is why he keeps thinking of him as a remarkable man and remains loyal to him.

Of course, there are critics that use Marlow's position as an unreliable narrator to question his interpretation of these final words, but to me, they do present a moment of self-knowledge where Kurtz comprehends the depths into which he had fallen, and also presents a damning condemnation of the whole colonial enterprise.

I'd love to give you a definitive answer, but that's just not possible. Those last words spoken by Kurtz have been the subject of endless debates and discussions about this story. In general, most of the opinions fall into two camps.  

The first is that at the moment before his death, Kurtz is hit with the full realization of all of the atrocities that he has committed while in the jungle. Putting people's heads on stakes is indeed fairly horrific. His words could be his spoken acknowledgement that he now realizes how much horror he has wreaked upon the people of the jungle.  

The second explanation that I hear the most is that Kurtz's words aren't technically his words. The words might be spoken by Kurtz, but it is Conrad's voice that we are really hearing. The story takes place in the later half of the nineteenth century. This places the story in the middle of the Age of Imperialism. Part of Europe's attitude during this time period was that their western civilization, culture, etc. was superior to everywhere else. There was this idea that western civilization was the pinnacle, and that it would eventually replace all of the "darkness" that existed in the "uncivilized" parts of the world. Kurtz was an agent of that colonization and committed horrific atrocities in the name of progress. Conrad is pointing out to readers that this notion of committing atrocities against other cultures is horrific. "The horror" is the entire concept of forcing your "superior" culture on a different culture.  

The first impression the reader gets is that Kurtz is alarmed, even repulsed, by the “primitive” behavior of the natives, their rituals (there are hints of cannibalism), their society—a primordial tribe without knowledge or benefit of “civilization.” But Conrad is going much deeper—he is letting the reader find out that Kurtz’ real discovery is the primitiveness of so-called civilized colonizing western cultures, the barbarism of humanity itself, the “horror” of being a human; therein lies the greatest literary irony: when Kurtz’ very proper and “civilized” fiancée asks about him, Marlow says “His last words were of you.”  The power of this novel-long, beautifully conceived allegory, a condemnation of Western Hegemony, is in his cry, “The horror!  The horror!”  We think of ourselves as being so dignified, so enlightened, compared to "backward" societies, and yet we have capital punishment, World Wars that must be numbered, indifference to world poverty, weapons capable of annihilating whole cities--Conrad's admonishment from another world echoes today like Kurtz' cry.

In Joseph Conrad's Heart of Darkness, Kurtz expires with the words "The horror! The horror!" These dying words have been analyzed as much as any in Western literature, despite the fact that Marlow, the narrator, explains and reflects on them himself. For Marlow, Kurtz's last words are "judgment upon the adventures of his soul on this earth."

Marlow's interpretation seems reasonable as far as it goes, but this is clearly not all there is to be said about Kurtz's dying words. One of the reasons Conrad's writing is so much analyzed is that he tends to prefer ambiguity to certainty. The horror to which Kurtz refers can be seen as life in general, his own life in particular, what he has done with that life, and, ultimately, the soul or character that allowed a civilized man to sink to such depths of depravity and insanity.

Whatever the reader thinks of Heart of Darkness, they are unlikely to have any quarrel with Kurtz's words about what he has seen and done. This would scarcely be the case if his last word had been the name of his fiancée, as Marlow pretends it was when he speaks to her. In the world described by Conrad, the horror of reality leaves no room for such sentimentality.