A Monster Calls is chock-full of clocks. Whenever Conor has his nightmare, there's one nearby, and it always reads 12:07. Let's take an inventory. There's:
They're all there for the purpose of summoning the monster, but they're also a reminder of time ticking away—and all too fast for Conor's taste.
Of course, the most important clock in the book comes at the very end, when Conor realizes he has only 21 minutes until his mother's death:
As the monster's hands gently but firmly guided him toward his mum, Conor saw the clock on the wall above her bed. Somehow, it was already 11:46 p.m. (20.32)
Time is finally running out, which is made all the more profound by the fact that we've been seeing clocks all along. 12:07 is one of the few things Conor's always been able to count on, even if its association with the dream is awful.
At the very end—both of the book and of his mother's life—Ness writes, "He knew it would come, and soon, maybe even this 12:07. The moment she would slip from his grasp, no matter how tightly he held on." We as the reader learn on the very last page, finally (though we suspected it earlier), the significance of the number. It may be when Conor's mom's life ends, but we have a feeling it will also be when the nightmare ends for good.
It's worth noting, too, that 12:07 comes just after the beginning of a new day. When Conor loses his mom, it's the beginning of a new life. Not only will he live in a different place physically, he'll live in a different place emotionally. It may be just as hard for the kids at school to accept that Conor's the kid with the dead mom as it was for them to accept that he was the kid with the cancer mom, but eventually he'll just be Conor again. A life in which he's no longer invisible is a new life indeed.