The admiraton one girl has for another. It could be to do with hair, body, make-up, car, clothes, career, talents etc. Completely non-sexual. Girl crushes are generally very short-lived, as girls move on very quickly from trends.
Tracy: I totally have a girl crush on Ashley Olsen, she's hot as.
Monica: Ummmm, I thought you had a girl crush on Sienna Miller?
Tracy: Ah, no! Ashley dresses way better!