Stuck-up describes a person who thinks they are better than everyone else, and shows it by not being friendly. The key is that both parts are there: the person feels superior, AND they act cold or distant because of it. Someone who is proud but still warm to people is not stuck-up. Someone who is quiet and shy is not stuck-up either — but they are often called it by mistake, which is worth knowing.

This is an informal, everyday word, and it is always an insult. You say it about someone, not to them, and almost never about yourself. It is a bit childish in flavour — school students use it a lot, about a classmate who will not talk to certain people, or who acts as if a group is beneath them. Adults use it too, but in casual talk, not in writing or at work. In a report or a formal complaint you would write 'arrogant' or 'aloof' instead.

One useful thing about the word: it often says as much about the speaker as about the person described. People call someone stuck-up when they feel looked down on. So it is frequently unfair — the 'stuck-up' person may just be nervous, or busy, or bad at small talk. Real speakers use it loosely, as a first reaction, not as a careful judgement.

It is normally used before or after a noun as a describing word: 'a stuck-up girl', 'she's so stuck-up'. It has no verb form and no comparative like 'stuck-upper' — you say 'more stuck-up'.