The set-up man is the reliever who puts the game in shape for the top reliever (the fireman or closer) to close the game. A setup man will usually be used in the 7th inning or later. He will often be brought in to start an inning, but sometimes may be asked to stop a rally.
The setup role is generally given to a reliever who is next in quality to the closer, and a team's top setup man will often move into the closer's role if the closer is unavailable because of injury, fatigue, etc. In former times, set-up men were not well-known, but with the advent of the hold, they are getting more attention.