The Black Sox refers to the White Sox scandal of 1919. Eight players conspired with gangsters to throw the World Series and they did indeed lose it. The eight players, dubbed the Black Sox because they gave the sport of baseball and the team a "black eye", were banned from baseball forever. "Shoeless" Joe Jackson (played by Ray Liotta in Field of Dreams and D.B. Sweeney in Eight Men Out) was one also blamed and he had agreed to go along with the plan. However, he backed out at the last minute and had the series of a lifetime with some spectacular postseason statistics. However he was still banned from baseball for life by the then-commissioner, I believe, Kenesaw Mountain Landis (someone correct me if I got the name wrong). None of them can even get into the Baseball Hall of Fame as a result.
If you want to learn more about the Black Sox, check out Field of Dreams with Kevin Costner or, preferably, Eight Men Out with Charlie Sheen, D.B. Sweeney, and David Strathairn. Field has some good information about the Sox and what happened while EMO is all about what actually happened.