A rebuff is what you get when you reach out to someone kindly and they push you away. The key is that the first move was friendly — an offer, a suggestion, an invitation, a hand held out — and the answer came back cold, short, or rude. If someone simply says no politely, that is a refusal, not a rebuff. The word carries the sting.

It works as a noun ('her offer met with a rebuff', 'a sharp rebuff') and as a verb ('he rebuffed all their attempts to help her'). The verb is the more common of the two in modern writing.

This is a formal, written word. You will find it in newspapers and reports — a country rebuffs another country's proposal, a company rebuffs a takeover offer, a minister rebuffs criticism. Ordinary people talking about their day would not say it; they would say 'she shot me down' or 'he wasn't interested' or 'they said no, pretty rudely'. So when you see 'rebuff', the writer has usually chosen it to sound a little distant and official — which is why it turns up so much in politics and business news, where the real feeling underneath is being kept at arm's length.