If you've ever driven a manual car and dropped into a lower gear, you've probably felt that sudden jolt when you let the clutch out. That's what rev matching is designed to prevent.
The technique sounds complicated, but the basic idea is surprisingly simple: rev matching makes the engine spin at roughly the speed it needs to be turning for the lower gear you're selecting. Modern performance cars can do this automatically, while old-school drivers can do it themselves with a quick throttle blip. Here's how.