Turn your nose up (at something) informal: to refuse to accept something because you do not think it is good enough for you: ● My children turn their noses up at home cooking.

The correct expression is "to turn its nose up", and it means to express one's disdain — the original idea is when one raises one's head slightly (so that the nose is higher than usual) and simultaneously looks down on something, in order to show one's contempt / disregard / disdain for something. The allusion here is to the traditional French rivalry with the British, their "traditional enemies" — so the image is of the French plane "turning its nose up" when landing in Britain. Of course, this is just a joke; in fact, the technciial reason is quite the reverse: Concorde had to have its nose UP for supersonic flight (to reduce drag), but the nose had to be lowered so the pilot could see the ground when landing and taking off.

Jesus, this expression is used in different ways. In your example, the girl or woman is expressing dislike, disdain, rejection. She might also be acting as if she's snobby or picky. If a guy turns up his nose at a job, he might also be expressing contempt for it. "I'm too good for that job." Does that help? dave