A "stuck up" person is someone who:
- thinks that they are better than other people
- thinks that other people are less important than them
- dislikes people who are poorer, less popular, or less powerful than themselves
Here are some example sentences:
I can't stand her. She acts like a stuck up little princess.
I guess I should go out drinking with them sometime. I don't want to be seen as rude or stuck up, you know?