This acronym usually refers to a Boi (as in the gay type - refer to boi) I (would) Like (to) F*ck (as in have sex with).
The connotation of boi implies that the one saying bilf is not a boi. Or in other words is not straight.
So basically, when a "straight" guy refers to a gay guy as someone the former would like to have sex with.
This is a definition that breaks gender norms and has been used among straight buddies, and has been accepted as a norm, regardless of its context, sarcastic or serious.
The straight guy points at the hot gay guy in the club and tells his buddy, "Hey there is a BILF!" His buddy laughs and concurs.