BLF is an acronym for Best Lady Friend. A female friend that's on the top of your close-friends list. It is a platonic relationship. Usually guys use this term to describe the relationship he has with the woman he hangs out with all the time, if she is not his girlfriend.
Vince: Yo Dude! You going out with Violet?
Dude: Nah, she's just my BLF.
Vince: O ok, 'cus I always see you guys together so I assumed she's your girlfriend or something.