A baseball league for boys, although girls have been known to play as well (there was one on my team for years, and she was better than most of us). Often the home of bad umpires.
There are several levels corresponding to the players' ages. Generally, Tee Ball (where "everyone's a winner" and there is no pitcher) is the starting level, and AA and AAA are the next two. After that it becomes much more challenging. In the lower levels, anyone can play, and it's a great way for kids to build friendships, but after Triple A it becomes much more competitive, tryouts are held, and in general only the best players continue.
The coaches were usually fathers of kids on the teams, and local businesses sponsored them (usually in the form of paying for uniforms with the businesses' names on them).
It's also worth mentioning that just as in the major leagues, there are two divisions/leagues: American and National.