Two monsters, both alike in dignity, in fair… oops, wrong book (although R&J could only have benefited from the addition of monsters). In all seriousness, we think the monsters in this book, with all their supernatural powers and keen ability to scare the pants off us, are serving a deep purpose. Back in the day, people used to blame supernatural, demonic spirits for mental illnesses and other health problems. And in A Monster Calls, the pit monster is connected to Conor's mother's cancer, while the yew tree monster is connected to Conor's own grief and bad behavior, just like in ye olden times. Only here, it turns out Conor's got all the power, and the monsters are merely there to play along.
Conor's monster is a version of the ancient Green Man myth.
Conor's mother isn't at peace with her own death, which is why she screams for Conor to hang on when the pit monster grabs her. In denying her death to Conor, she's also convinced herself she can prevent it with enough willpower.