Physically, Kurtz dies of the unspecified "fever" that Marlow knows has been killing men in the Congo. When Marlow encounters Kurtz, Kurtz is very ill and near death.
But Marlow differentiates between the body of Kurtz, which he calls the "hollow sham" which will soon be buried in the "primeval earth," and his soul. Kurtz's death, Marlow implies, also comes from facing the soul truth of the futility of his life:
I saw on that ivory face the expression of sombre pride, of ruthless power, of craven terror—of an intense and hopeless despair. Did he live his life again in every detail of desire, temptation, and surrender during that supreme moment of complete knowledge?
After the above insight Marlow has, Kurtz cries out, "The horror! The horror!" and soon dies.
In Marlow's reading of Kurtz, he sees the man as dying when he realizes, with despair, that everything he has desired and worked for—money, power, prestige—is all false, all as much a "sham" as his outward physical body. Marlow has mixed feeling about Kurtz: he is, on one hand, the heart of darkness, a ruthless murderer who would stop at nothing in the pursuit of profit. But Marlow also admires him for his courage in being able to tear away the veil of illusion and face the truth, both the truth that greed and evil are the only reasons the Europeans are in Africa and the truth that the lust for money and power that drives their imperialism is a worthless value. Marlow observes of Kurtz's final words about the "horror,"
He was a remarkable man. After all, this was the expression of some sort of belief; it had candour, it had conviction, it had a vibrating note of revolt in its whisper, it had the appalling face of a glimpsed truth.
Conrad contrasts Kurtz's ability to look reality in the face, even if it ultimately kills him, with the illusions that women like Kurtz's unnamed "intended" hold that imperialism is a noble and idealistic venture.