Hit and Run
The runner goes, and the batter must swing to protect him.
How it actually works. The runner leaves as if stealing, which pulls either the shortstop or the second baseman toward the bag to take the throw. The hitter's job is to make contact, ideally on the ground and ideally through the hole the middle infielder just left. He swings at almost anything, because a take turns the play into a straight steal with the runner exposed and the count in the pitcher's favor.
Why it is done, and when it is wrong. The play is doing two things at once and people usually only notice the first. It stays out of the double play, which is the obvious part. The larger part is that it manufactures a hole in a defense that was standing in the right place, because a middle infielder cannot both cover second and field a ground ball up the middle. That is why the call is made with a contact hitter rather than a good runner. The runner's speed barely matters. The hitter's ability to put the bat on a bad pitch is the whole play.
What people get wrong about it. It is called the hit and run and it fails as a run and hit. If the hitter misses, the runner is stealing on a count the manager chose rather than one he liked, usually against a catcher who was already looking. A swing and miss on a hit and run with a slow runner is the worst single outcome available in an inning, and it is why the play is called on counts where a strike is likely, most often 1-0 and 2-1, and almost never with two strikes.
At Little League and travel ball. At youth levels a straight steal succeeds so often that the hit and run is usually the worse play. Its real use is teaching hitters to swing at strikes and run the bases with their heads up, and coaches should be honest that this is what they are getting out of it.
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