When a player sees his position is hopeless, and ends the game before checkmate.
When a player realizes that he is going to lose and graciously gives up the game without waiting for a Checkmate. When resigning, a player can simply say, "I resign", or he can tip over his King in a gesture of helplessness.
To forfeit the game. In Match Play: One must specify whether one is forfeiting a single game, a gammon, or a backgammon, with the agreement of one's opponent. In tournament play: Resignation cannot occur before contact is broken.
To concede loss of the game. A resignation is usually indicated by stopping the clocks, and sometimes by offering a handshake or saying "I resign". The traditional way to resign is by tipping over one's king, but this is rarely done nowadays.
To recognize your defeat. You can't resign at tournaments.
to give up a losing game before mate. It is polite to do so, and perhaps less painful for yourself, but some players play on in the hope of their opponent blundering.