At first, Conor thinks that the monster's nothing more than a dream. There's certainly something dream-like about how the monster first appears to Conor: by the moonlight near the old church and graveyard. Under the circumstances, Conor can be forgiven for thinking that the strange apparition outside is all just a dream. But once he realizes that the monster's real and means him no harm, Conor gradually starts to develop a close relationship with him.
The monster is incredibly wise, and through the stories he tells Conor, imparts his wisdom on matters of life and death. In turn, this allows Conor to gain a greater degree of self-understanding, making him better able to deal with the various issues that cause problems in his life, such as his mother's terminal illness. The relationship between monster and boy becomes one of mentor and student, of a moral guide leading his young charge to face up to the truth of his situation, thus liberating him.
Initially, Conor views the Monster as a threat. It appears to want to eat him and it makes threats about what will happen should Conor not share a "fourth" tale with him, which Conor interprets as a threat on his life. Conor also derides the Monster's interest in telling stories, since he views stories as a childish pastime.
However, as the novel progresses, Conor comes to view the Monster's visits as a comfort. The stories entertain him, and he learns about the nature of life and the human condition from them. When he believes the Monster will not appear to him again, he is afraid because he genuinely enjoys the visits.
The Monster ultimately becomes Conor's greatest comfort. It confesses at the end that it came to "heal" Peter and prepare him for the loss of his mother. The threats the Monster made about Conor having to share his tale were not about literally eating Conor, but about the guilt he felt eating him up emotionally.
When Conor first meets the monster, he believes the monster is his nemesis; however, over the course of the novel, the monster goes from being threatening to becoming a comfort to Conor as Conor faces his mother's impending death from cancer. When Conor first meets the monster, the monster is menacing: "the monster roared even louder and smashed an arm through Conor's window, shattering glass and wood and brick" (page 8). When Conor says he is not afraid of the monster, the monster replies, "You will be...Before the end" (page 9). Then, Conor remembers the monster trying to eat him alive before he wakes up from his nightmare.
In the middle part of the book, the monster says that it wants to talk with Conor. When Conor asks the monster what it wants from him, the monster replies, mysteriously, "It's not what I want from you, Conor O'Malley...It is what you want from me" (page 34). Conor still feels strangely calm around the monster, even though he is having a nightmare. The monster tells Conor that it will tell him three stories and that Conor will tell him the fourth. The monster says, "You know that your truth, the one that you hide, is the truth that you are most afraid of, Conor O'Malley" (page 38). The truth that Conor hides is that his mother is sick with cancer and that Conor has no one around him to comfort him, as his relationships with his father and grandmother are not good.
In the end, after Conor tells his story, the monster comforts him. Even though Conor wants the monster to heal his mother, the monster says, "I did not come to heal her... I came to heal you" (page 193). By forcing him to listen to its stories and tell his own, the monster has healed Conor and prepared him for his mother's death.