1) A girl who is interested in things considered geeky
by mainstream society.
2) Usually refers to girls who are interested in computers, and technology in general, can also be used for girls who do things not considered "cool" by everyone else.
3) A compliment to girls who are proud to be geeks.
Person 1: What's up with that chick sitting on the floor with the computer?
Person 2: Oh, that's our resident geek girl.
Person 1: Well, we've got jocks, preps, nerds, burnouts, and a few geek girls hanging out in the library.