What is the literal meaning of "One Flew Over the Cuckoo's Nest"?

The film's title was derived from a familiar, tongue-twisting Mother's Goose children's folk song (or nursery rhyme) called Vintery, Mintery, Cutery, Corn. The ones that fly east and west are diametrically opposed to each other and represent the two combatants in the film. The one that flies over the cuckoo's nest [the mental hospital filled with "cuckoo" patients] is the giant, 'deaf-mute' Chief:

Intery, mintery, cutery corn,
Apple seed and apple thorn,
Wire, brier, limber lock,
Three geese in a flock;
Along came Tod,
With his long rod,
And scared them all to Migly-wod.
One flew east, one flew west,
One flew over the cuckoo’s nest.—
Make your way home, Jack.

https://etc.usf.edu/lit2go/74/nursery-rhymes-and-traditional-poems/5204/intery-mintery-cutery-corn/