Charlie Marlow loves maps. He wants to become an explorer so he can fill in those blank spaces on the maps. Upon acquiring a steamboat with the Company, he begins his journey into the African interior. This is a lovely little conflict-free initial situation. Although, with comments like "morituri te salutant" ("we who are about to die salute you") (1.4), we have a feeling there's some conflict coming soon.
Marlow hears about Kurtz and almost immediately becomes obsessed with him. To Marlow, Kurtz answers all sorts of problems: the eerie silence of the jungle (by having an eloquent voice), the shenanigans of the native Africans (by "taming" them), the chaos of the wilderness (by acquiring ivory), and the moral ambiguity of the interior (by making himself into a kind of god).
So, where's the conflict? To find this paragon and bring him back to civilization, Marlow has to go on a perilous journey—both physical and mental. Plus, there are cannibals.
All Marlow wants to do is be BFFs with Kurtz (and bring him home), but he just runs into problem after problem. First, he can't get his steamboat moving up the Congo. Second, a bunch of Company peons are trying to undermine Kurtz.
And third, Kurtz is a total loony who orders Marlow's steamboat to be attacked because he doesn't want to leave the interior. Oh, and the native Africans don't want him to leave either.
Kurtz tries to escape from his hut right before Marlow and company are scheduled to bring him home, but it's not much an escape since the guy is half-dead already. Marlow catches up to him and, at this point, has two options: either let him go and allow Kurtz his victory, or follow Company orders and bring him back.
Marlow goes with option two, and the next morning they make a successful escape from the restless Africans. It's all very climactic.
Right when you think Marlow is going to succeed in his mission of bringing Kurtz back to civilization … Kurtz dies. In fact, he dies in complete agony, first going blind, then raving incomprehensibly, then finally seeing visions as he expires. His last words—"The horror! The horror!"—pronounce his final judgment on his world.
Okay, we admit that a death sounds a lot more like a climax than suspense. Here's where he think the suspense comes in: with Kurtz dying in this dramatic way, we're left wondering what's going to happen to Marlow. Is he going to go back to his regular Company life, just a regular imperialist working stiff? Or has he actually learned something from his trip into the heart of darkness?
Marlow returns safely to Belgium, only to find that everything is petty and small when compared to the horrors he experienced on the Congo. (Wait, isn't that a good thing?) He has one final task before he can finally move on: handing over Kurtz's letters to his Intended, i.e. fiancée.
For some reason, everyone back home still thinks of Kurtz as a saint and martyr and all-around good guy—particularly the Intended, who goes on and on about how awesome Kurtz is. Marlow doesn't correct her. In fact, he lies right to her face, leaving us wondering what kind of lesson he's learned at all.