If you were like us, when you first read the title you thought it had something to do with the main character being a "big cheese" or something like that. But it becomes obvious pretty quickly that Adam isn't a big cheese.
Over the course of the novel we realize that I Am the Cheese is a reference to the popular children's song "The Farmer in the Dell." If for some reason you've never heard this song (like you weren't born on this planet), go have a listen. The last line of the song is "The cheese stands alone." So by saying "I am the cheese" (31.39), Adam is saying that he knows he is alone. Without parents, friends, or anyone who truly cares for him, he is by himself in the world, even in the world of his imagination.
If you look at the song more closely, you see that it's about choosing. Each character in the song, from the farmer to the rat, gets to make a choice. The cheese is the only one who doesn't (cheeses are inanimate objects, after all). In this sense, Adam really is the cheese: he lacks control over his own destiny. Everything about his family's life was determined by government officials, and now he is in the custody of people with the power to end his life.
Identity and isolation are two of the most important themes in this book, and the title, I Am the Cheese, touches on both of them. It's really the most perfect, most devastating title.