Baseball, by the Rules
For more examples, click here, though note that this type of play is tricky to filter down to; the vast majority of clips here should be infiled-fly-rule-related, even if the commentary doesn't explicitly say so.
The Infield Fly Rule
The batter hits a lazy pop-up that drifts over the infield. The fielders converge underneath it, and the batter jogs towards first. But while the ball is still in the air, the umpires are already signaling that the batter is out. What’s going on? Welcome to one of baseball’s most notorious rules: the Infield Fly Rule. Often cited as a rule that’s too complicated for its own good, really all the infield fly rule is doing is preventing the defense from turning cheap double plays.
How? Well, imagine a scenario where the offense has multiple runners on base, all of whom would be forced to the next base on a base hit. The batter hits a towering pop fly over the infield. The runners go back to their bases as they know the ball is going to be caught. Except... whoops! It's not caught. The ball drops in front of an infielder, who picks it up and now has the runners dead to rights. If you're the defense, this is a heads-up play. If you're the offense, you're... much less enthusiastic about the outcome.
Enter the infield fly rule. Said rule basically looks to short-circuit a “cheap" double play by saying that once a ball is popped up in the general vicinity of the infield, the umpires will immediately declare it as an out, no matter what actually happens. The rule only applies in specific situations:
As you might imagine, that last point can occasionally lead to some differences of opinion, as it's the only part that relies on an umpire's judgement. Normally, though, it's an easy call to make, and everyone can move on with their lives.
Any runners on base prior to the infield fly have the chance to tag up and advance once the ball is caught (as long as the catch isn't the third out, of course); however, since we’re talking about the ball still being in the infield (most of the time), it’s extremely unlikely that they would do so. As such, play will continue with the runners starting from their previous bases.