This is a baseball phrase used to describe a pitch thrown when the batter has full count. A full count means there are two strikes and three balls. The payoff pitch is the final pitch of the at-bat, though if the ball is fouled off, the at-bat will continue. The concept behind its name is that the pitch will result in either a strikeout or a walk. The most common time to use this phrase is at the end of an inning or at the end of a game, where a single pitch can make a big difference. For example, if the bases are loaded and there are two outs, and the batter has a full count, the payoff pitch determines if a run scores or if the inning is over.
The payoff pitch is not one type of pitch; it applies to the situation the pitch is being thrown in. Every pitcher has a different strategy for dealing with this situation. Some managers will call timeout to make sure the entire team is prepared just in case there is a hit, and to help the pitcher choose a pitch, or just to give a pep talk. The best pitchers enjoy the pressure and typically perform will when asked to throw a payoff pitch.