It's "One Flew Over the Cuckoo's Nest".
The meaning of the title is actually explained by the book. It's a chant the narrator's grandmother used to say:
One flew east, one flew west,
One flew over the cuckoo's nest.
O U T spells "out",
Goose swoops down
And plucks you out.
Chants like this are often used by children to select one player for a specific role in a game. One player would chant, while pointing at each player in turn in time to the chant. Whoever was being pointed to on the final syllable was "out" -- i.e., eliminated, and the process continued until only one player was left.