The infield fly rule: imagine that there's a runner on first base, and the batter hits a weak little popup to second. The correct thing for the second baseman to do is to catch the ball, putting the batter out.

However, a clever second baseman could theoretically just let the ball drop to the ground at his feet. At this point, the ball is in play, and the runner at first faces a force out at second. So by letting the ball drop, picking it up, stepping on the base, and throwing to first, the defense could pick up an extremely cheap double play on what should have been a simple fly out.

The infield fly rule prevents that specific little bit of cheapness. If it's obvious that it's a weak little fly ball to the infield, the umpire can simply call the batter out, whether the defense actually catches the ball or not, on the assumption that if they don't catch it, they're trying to cheat in that specific way. It only applies if there's a runner on first with fewer than two out, which is what makes the rule look more complex than it really is.

There. Now you know about the infield fly rule. :-)