During the war, professional baseball for women began as a way for baseball team owners to keep some income coming in while many of their brightest stars were involved in the war.
Here is the link for the real website for the league: http://www.aagpbl.org/ It is fascinating!
Here is an overview of the League: http://www.seanlahman.com/baseball-archive/womens-baseball/
Here is a clip from A League of Their Own, in which director Penny Marshall tells the story of the League from a historical fiction viewpoint. The older ladies at the beginning of this clip were actual players in the League and were playing on the field at the Baseball Hall of Fame in Cooperstown New York. A permanent exhibit on women in baseball has been in place there since 1988 and is depicted at the end of the film.