From BR Bullpen
An exhibition game is a game which does not count towards the final standings or the league championship. It can be organized between two teams in the same league, between teams from different leagues that do not normally play each other (for example, a major league team and its AAA affiliate, or a major league team and a foreign squad), or between an organized team and either a barnstorming team or a squad put together just for the occasion.
Exhibition games serve two purposes: to provide training for players in advance of the season (all Grapefruit League and Cactus League contests held in spring training are exhibition games) and/or to raise revenue. The revenue raised can either be for a worthy cause - in the first half of the 20th century, teams would often play exhibition games to collect funds for the family of a deceased or severely injured player, or in support of the war effort - or for operating revenues. Often, minor league teams will have an exhibition game built into their affiliation contract with a major league team to raise additional revenue.
Exhibition games were very frequent, before, during and after the regular season, until the 1960s. They are much more rare today outside of spring training, because of the 162-game schedule which leaves few open dates, the introduction of interleague games which have eliminated the interest once associated with city series, and the risk of injury to highly-paid players. The annual Hall of Fame Game, one of the most famous in-season exhibition games, was canceled in the 2000s for these reasons.
Another longstanding exhibition contest was the Mayor's Trophy Game.