Bats in the belfry meaning

It refers to being crazy or eccentric behavior 

Bats are erratically flying mammals and 'belfries' are bell towers 

Bats in the belfry refer as someone who acts as though he has bats careering around his topmost part, that is, his head.

is to be crazy an old woman with bats in her belfry

To be crazy; to act, think, or behave in a foolish or nonsensical manner