This quote is a verse from "The Farmer In The Dell", a song that Adam sings during the book:
The cheese stands alone The cheese stands alone Heigh-ho, the merry-o The cheese stands alone
He sings many of these songs throughout the novel. The song contains several characters, each taking someone with them when the farmer leaves, yet the cheese has nobody.
Adam believes that he is the cheese. He is alone in the world, his mother dead and his father missing, and he lives in a hospital. He thinks that he is not wanted anymore. Also, as in other works by Cormier, there is a dual meaning to the title. The words "I am the cheese" may also represent Adam's feelings of entrapment: he is the bait used to lure his parents to their murders.
Another point is that his father had taught him the song, possibly in a way to reinforce the new name, 'Farmer', they had adopted.