Rev matching is the process of adjusting the engine speed while changing gears, so that both sides of the clutch are turning at the same speed when the clutch is being engaged.
Imagine the opposite: having the engine at idle and releasing the clutch. As the clutch engages, the engine and gearbox speeds are pulled together until they are turning at the same speed. Done quickly, this is generally accompanied by a sharp jerk as the vehicle speed rapidly adjusts.
The advantages are a smoother clutch-in and somewhat less clutch wear.
As for how you know what the right RPM is, that’s a matter of experience with the particular vehicle.
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