* Gear Ratios: Each gear in a manual transmission has a different gear ratio. Lower gears (1st, 2nd, etc.) have higher ratios, meaning the engine spins faster for a given wheel speed. Higher gears (4th, 5th, etc.) have lower ratios, meaning the engine spins slower for the same wheel speed.
* Shifting: When you shift to a higher gear, you're effectively telling the transmission to connect the engine to the wheels through a lower ratio. This means the wheels will now turn faster for the same engine speed. However, the engine's speed doesn't instantly adjust.
* Momentum: The car has momentum from its previous speed. To keep moving forward, the engine needs to continue to provide torque, but in the higher gear it needs to provide that torque at a lower RPM.
* The Rev Increase (Temporary): Because the engine was previously spinning at a higher RPM suited for the lower gear, and the higher gear requires a lower RPM, there's a brief moment where the engine speed is too high for the new gear. This results in a temporary increase in RPM as the engine adjusts. Then the driver releases the clutch. Once the clutch is fully engaged, the engine speed drops to an RPM appropriate for the new gear and the car's speed.
In short, the revving is a temporary consequence of changing the gear ratio and the time it takes for the engine speed to match the new rotational demands of the wheels. A skilled driver smoothly matches the engine speed to the wheel speed (via throttle control and clutch work) minimizing this revving effect. Automatic transmissions manage this transition automatically, hence there isn't this noticeable rev.
