It's 12:07 a.m. Conor wakes from his nightmare, the one he has every night, and hears someone calling his name. When he looks outside, he sees that the yew tree near his house has turned into a monster. The monster comes to Conor's window and does a bunch of monstery stuff, like growling and yelling, but Conor's not impressed. After all, it's not the monster he was expecting. Ness is setting up the basis for the story here: we have the time of the dream, the partial content of the dream, and the arrival of the first monster, all of which will become key elements in the book.
The biggest conflict in Conor's life, by far, is the fact that his mom is dying of cancer. She's had round after round of chemo, but none of them have worked. The sicker she gets, the more the kids at school either bully him or ignore him. On top of that, he has to go stay with his grandma when his mom goes into the hospital, and he's not a fan of the old lady at all. Life doesn't get much more complicated than that.
The deal the monster made with Conor is this: he'll tell Conor three stories on successive nights, after which Conor has to tell the monster about his nightmare. Sure enough, after the monster's told the stories, Conor is forced to face the monster he's actually afraid of: the one that pulls his mother off a cliff in his recurring dream.
He tries to save her, but the pit monster is too strong. Losing his grip on his mother is a pretty big crisis, the one Conor believes leads to her death. Once he's told the monster the truth, Conor finally admits that he had to let his mother go because he was so exhausted, and the monster allows Conor to fall asleep in its branches. He no longer has to remain vigilant against his nightmare, so he can get some peaceful Zs.
By the time Conor's grandmother finds him asleep in the roots of the tree—which is now just a tree again—his mother is almost gone. Grandma hustles Conor into her car and takes him to the hospital, where we see that his mother's death is inevitable. The thing everybody's been denying is finally about to happen, and they're all ready to end the pain, even though of course it's awful.
Conor takes his mother's hand for the last time, and she wakes up just long enough to tell him it's okay to be angry. The monster comes into the room and reminds Conor to speak the truth, so he tells his mother he doesn't want to let her go. She closes her eyes with a few minutes left before 12:07, at which point we finally know how the story ends: she's not going to get better, she's going to pass away. Even though we don't get to see the actual moment of her death, we know it'll go down at seven minutes after twelve.