A toffee-nosed person acts like they are better than everyone else — usually because of money, family, or the school they went to. It is not about being rich; it is about the attitude. The word carries the speaker's dislike inside it, so you cannot use it about someone you admire. You can also call a place or a thing toffee-nosed: a toffee-nosed restaurant, a toffee-nosed accent, a toffee-nosed neighbourhood. Then it means the place is full of that attitude, or is trying hard to look expensive. This is British English, informal, and a little old-fashioned now — you will meet it in books, in older TV comedy, and from older speakers more than from young people, who are more likely to say stuck-up or posh. It is rude but not a strong swear word; it sounds more mocking than angry. Note that posh on its own just describes class or expense and can even be a compliment, while toffee-nosed is always a complaint about how the person behaves.