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".