This is a baseball term used when a player from a semi-professional minor league team is brought onto a professional major league team. Every team in Major League Baseball has affiliated itself with many semi-professional, or minor league, teams of varying skill level. If the skill level of a player is high, and he has advanced through the necessary skill levels of the minor league system, he may be "called up" to a major league team. There are specific hurdles a player must clear in the minor league system in order to be qualified to advance, although there are some rare prospects, or rookies, who skip the minor league system and start on a major league team.
This term stems from the distinction made between minor and major league teams--that the minor league teams are below the major league teams in skill level. The minor league system has been around about as long as the major leagues have, and minor league teams have close relationships with their affiliate organizations. This allows the professional team to develop players of varying skill levels and advance them through the system. A minor league player's goal is always to get "called up". Major league teams also use their affiliated minor league teams as a place for veteran players to rehabilitate their injuries. Once the player is better and in good form, the team will "call up" the veteran, though in this case it is a formality.