viscous sticky stuff prepared from holly bark and used to catch small birds, mid-15c., from bird (n.1) + lime (n.1). Used as rhyming slang for time (especially time in prison) by 1857; hence bird (n.) "jail" (by 1924).
bird-brain
bird-cage
bird-dog
birder
birdie
bird-lime
birdman
bird-seed
biretta
Birmingham
Biro