This is a baseball term which refers to a substitute pitcher. A substitute pitcher is called a relief pitcher because they are coming into the came to relieve the current pitcher of their duties. A relief pitcher differs from a starting pitcher in that a starting pitcher will not come in mid-game, while that is the express purpose of a relief pitcher. However, there are times, mostly in the playoffs, where a starting pitcher may be used in a relief role. A relief pitcher will be used for a variety of reasons, most of which are at the discretion of the manager. A starting pitcher may be subbed out for a relief pitcher if they: are tired, less accurate, pitching slower, lost a "feel" for the game, or otherwise not performing as well as they should for whatever reason.
A manager may also choose to bring in a relief pitcher if a batter is particularly good against the current pitcher, or the batter is left/right handed and the current pitcher does not pitch as well to that side of the plate. To replace a starting pitcher, a manager will make a call to the bullpen, where relief pitchers warm up, get one (or two or three) pitchers warmed up, and then bring one in when the time is right. A subset of relief pitchers "closers." These are pitchers who come in for the last, or last two innings, in order to get outs quickly.