The set-up man in baseball is a relief pitcher whose responsibility is to bridge the gap between a team's starting pitcher and its closer. The set-up man is typically the second best reliever on a pitching staff.
To understand the role of a set-up man, one must first understand the closer. When a team has a small lead late in a game, it is customary to call on the closer. The closer is typically the team's best relief pitcher, and he is usually required to get the last three outs or less of a close game. It is rare for closers to work more than one inning, and they almost never work more than two.
The starting pitcher, whose job it is to pitch effectively as deep into the game as possible, often does not have the stamina to last until the eighth or ninth inning. When the starting pitcher must leave the game, and it's not a situation in which the closer would normally be brought in, a team generally calls upon its middle relievers.
The set-up pitcher is simply the best middle reliever a team has. The critical situations in which closers are used in the eighth or ninth inning are the same situations in which a set-up pitcher would be used in the seventh or eighth.
The set-up man was once considered an undervalued position, possibly because there were no statistics to measure his effectiveness aside from the earned run average, which is used for every type of pitcher and did not reflect the specific requirements of the set-up man. Starting pitchers are usually measured by their wins, while closers are credited with saves when they protect a lead at the end of a game, but the set-up pitcher had no such statistic.
A new statistic, the hold, was created with the idea of measuring the effectiveness of a set-up man. The hold is subject to similar requirements as the save. In order to receive a hold, the pitcher must enter the game in a "save situation" - i.e., the conditions under which a save may be recorded, which is basically a lead of three runs or less - and leave the game with the lead still intact. The hold is not considered an official statistic by Major League Baseball, but it is often used in player evaluation and fantasy baseball.