The phrase implies a subtle way of looking down on things with a hint of disdain or contempt. At the party, he turned his nose up at the homemade snacks.
Pro Tip 2/3
Not Literal
This idiom isn't about physically moving your nose, but a metaphor for rejecting something you feel is beneath you. She turned her nose up at the budget hotel accommodations.
Pro Tip 3/3
Informal Usage
Used in casual conversation, it may be too informal for serious writing or formal speeches. Even though it was his favorite as a child, he now turns his nose up at canned soup.