This expression means; To be acting crazy.

This idiom is attributed to an old folk belief according to which
animals, such as birds, live in the minds of the mentally ill.
Originating from the middle ages when it was thought that people
of unsound mind literally had birds nesting in their heads and flying
around, causing madness.
A similar phrase is “eine Meise haben,” meaning “to have a tit.”
Meise translates to the English bird “tit.” Here the word “Meise”
originates from the yiddish “Maase” or “Maise,” meaning “story.”
Over time the definition evolved from story into “rambling” or
“silly” speech. If somebody has a bird, the implication is that they
are acting crazy.