I'm only a novice animator, but I'd explain it like...just think of it economically, from a frame-saving point of view. You could have a character move out of the scene normally, and you'd have to do every frame of them running over to the side and exiting...or you could have 'em wind up and suddenly "stretch" out of the scene, which basically eliminates most of those middle frames. In other words: a stretch or a smear should replace the movement from point A to point B.
Of course, that's just * basically * what it is; professionals use them more for their dynamic motion than for cheats (although a good cheat is a precious thing~). If you're having trouble understanding it, visualizing it, or planning it out, I'd suggest looking at frame-by-frames of old cartoons like Tom & Jerry; anything with lots of goofy chase scenes. ^^