If you rebuff someone, you reject or snub him. You might decide to rebuff a classmate's invitation to the dance after hearing him gossip meanly about a friend.
Although the verb rebuff is a somewhat old fashioned one to use for social relationships, it's still common in the world of diplomacy. One country's rebuff of another might start a war, or end peace talks, or otherwise reverberate through the world of international relations. You can also use rebuff as a noun — deliberately ignoring your sister's text message is one example of a rebuff. The Italian root word, ribuffo, combines ri, expressing opposition, and buffo, "a puff."