How is the title of Heart of Darkness justified?
The "Heart of Darkness" which pervades the story is not a place or a thing; it is a feeling that comes from looking inside one's self without the constraints of conscience, morals, or societal expectation of ethical behavior. Marlow himself experiences it, mentioning it not only as a description of the jungle itself (traveling "deep into the heart of darkness"), but as a consequence of living without that civilized restraint; Marlow fears that anyone who is not destroyed by that experience would become as evil as Kurtz, even himself.
"Kurtz discoursed. A voice! a voice! It rang deep to the very last. It survived his strength to hide in the magnificent folds of eloquence the barren darkness of his heart. Oh, he struggled! he struggled! The wastes of his weary brain were haunted by shadowy images now..."
(Conrad, Heart of Darkness, gutenberg.org)
The imagery of the title is straightforward; the interior jungle is a dark place, without civilized morals, and exposure to that almost nihilistic place degrades one's own moral strength. However, it also refers to the mental state of Kurtz when he leaves; his mind and soul are now a part of the jungle, and cannot survive outside it. Since Kurtz has hidden the degradation of his heart from others, it is only his heart (soul, ethical mind) that is dark, while his outward appearance remains "light" until his heart is revealed (seen in the Russian, who admires Kurtz without fully understanding him).
When the novel opens, the narrator, Marlow and his companions are taking a boat trip on the River Thames. It's a lovely sunny day in a peaceful place, but Marlow suddenly remarks that London too "has been one of the dark places of the earth." His remark follows the narrator's allusions to the days of the conquering explorers, like Sir Francis Drake and his ship the Golden Hind.
[The Thames] served all the men of whom the nation is proud, from Sir Francis Drake to Sir John Franklin, knights all, titled and untitled...
After another narratorial passage, Marlow explains he is speaking of the ancient days of Roman rule in England:
"I was thinking of very old times, when the Romans first came here, nineteen hundred years ago--the other day..."
All through the novel, the greatest "darkness" is associated with all ages of colonialism and conquest.
Marlow, travelling into the Congo, eventually finds the darkness is not in the "dark continent" and its people, but rather in the evils that colonialism has brought to it. However, Kurtz's last words "The horror! The horror!" seem to extend beyond his own horror at what he has seen and done, into a comment on the human condition itself. So you can broadly see the novel as an attack on colonialism, but Conrad goes further to suggest that the "heart of darkness" can be found in the human heart and all human evil.