Triple-A refers to the highest level of play in minor league baseball

Minor league baseball

Minor league baseball is a hierarchy of professional baseball leagues in the Americas that compete at levels below Major League Baseball and provide opportunities for player development. All of the minor leagues are operated as independent businesses...

 in the United States and Mexico.
Triple-A teams' main purpose is to prepare players for the Major Leagues:
Both young players and veterans play for Triple-A teams:

Players at this level who are on the 40-man roster of a major league team can be invited to come up to the major league club once the major league roster expands on September 1 (though teams will usually wait until their affiliates' playoff runs are over, should they qualify).