The Negro Leagues were were African-Americans played baseball during the segregation era until Jackie Robinson broke the color barrier in major league baseball. The Negro Leagues continued for a few years, but largely had ceased to function by the late 1950's, as most of the talent had made it into major league baseball.
And, oh, what some incredible talent major league baseball missed out on during that era. Josh Gibson, a catcher, was the Babe Ruth of Negro League baseball with over 800 career home runs. Satchel Paige, Hank Aaron, and many others got there start in baseball through the segregated leagues.
Interestingly, many clubs were owned and managed by African-Americans in an era when there was very little enterprise available for African-Americans. To learn more, go to the website or watch Ken Burns baseball documentary. If you are ever in Kansas City, its worth seeing. Its a great little museum.