I'm just starting to learn it myself, so forgive me if I make a mistake here and there. I've found that it's a stat that is used to try to identify if a player is getting lucky or unlucky. Basically it identifies what percentage of balls hit in play result in hits.
From what I understand, the MLB average is somewhere between .290 and .300. Really good hitters like Manny seem to be able to control where they hit the ball and have career averages closer to .350, so BABIP isn't as good of a predictor for hitters. Pitchers don't seem to be able to control where a ball is hit in play and both the great and the crappy pitchers all seem to be within the .290 to .300 range, so BABIP is a better stat to use when analyzing pitchers.
So, let's use Cliff Lee, CC Sabathia, and Edinson Volquez for examples:
Lee's BABIP is currently .224, which is much lower than the normal range. That means hitters are only hitting .224 against him when they put a ball in play. Based on normal BABIP, the law of averages would say that Lee is getting lucky and soon that .224 is going to go up, which means more batted balls are going to turn into hits instead of outs.
Sabathia's BABIP is currently .379, which is much higher than normal and means that he is getting unlucky and soon more of those batted balls are going to result in outs, not hits.
Volquez's BABIP is currently .287, which is pretty close to the normal range and means that he appears to be neither luck or unlucky, but right where he should be.
That's my take.