The last three paragraphs of Atonement basically tell you that everything in the book was made up. We knew this already of course (it's a work of fiction, after all), but it's still a little bit of a shock.
Specifically, the last paragraphs are where Briony tells us (indirectly, but pretty clearly) that in the novel we've just finished reading, some of the plot isn't "really" what happened.
Specifically, Robbie and Cecilia didn't reunite and live happily ever after. Robbie died on the Bray Dunes on June 1, 1940 of infection, and Cecilia died a few months later in a bombing during the German airstrikes on London. Furthermore, Briony never actually walked to her sister's apartment, as she says she did in part 3. Instead she simply returned to the hospital and just imagined herself going to her sister's.
"How could that constitute an ending?" Briony asks four paragraphs from the end after explaining why she changed the facts. The ending she's referring to, though, isn't the end of the book we're reading, just the end to the book she wrote. We get the conclusion she withheld from her novel anyway. The end of Atonement, then, repudiates itself, or tries to: It tells you that it's not the end that should have been.
Briony also points out that she did not allow her lovers to forgive her. She is also, though, thinking of another draft, in which we end with "Robbie and Cecilia, still alive, still in love, sitting side by side in the library, smiling at The Trials of Arabella. It's not impossible." It is the last thing Briony shares with us before going to sleep and the whole book wraps.
We never read that draft though. Briony either changed her mind, or else her vascular dementia prevented her from writing it. On the other hand, though, we do still see that last image through Briony mentioning it. In that one sentence at least, Cecilia and Robbie are alive and in love until the very end.
So why have the tricky ending? Why make us happy and then sad? Why the bittersweet confusion? Well, in the first place, it ties up the themes neatly—Briony atones for making up a bitter story about Robbie by making up a sweet story about Robbie. And, in the second place—it's just kind of phenomenally tear-jerking. The book is sort of a tragic romance, and one of the things you're supposed to do at the end of a tragic romance is bawl your eyes out. Giving you the sad ending might have tugged on your heart, but giving you the happy one and then sucker punching you—that's just brutal.
The last line of the novel is "But now I must sleep." Sleep reminds us of dreams, which is fitting since Briony has essentially dreamt up the whole novel. It suggests death too, though, which is coming for Briony shortly. But it's also an announcement that she's going to put down her pen. And what happens in a novel about writing when the writer stops writing? Nada. It's the end.