Meaning

noun a short stout club used primarily by policemen

noun male goat

originUncertain, but probably extracted from Scots billypot (“a type of cooking pot”), perhaps originally from the name Billy, a diminutive of William. The condom sense from the E-Rotic song Willy, Use a Billy... Boy, referring in turn to Billy Boy, a German brand of condoms.

Etymology from Wiktionary, CC BY-SA 3.0