Excuse my ignorance, matching Revs to what ?
If you're traveling at 40mph in 3rd, lets say your rpm is going to be around 3000. Now if you were in 2nd at the same road speed, your rpm would be more like 4500, as soon as you press the clutch pedal (in 3rd) your revs will fall as the engine has lost connection with the wheels, so let's say you slowly let the clutch back out in 2nd and the revs have already dipped to 2k, your engine has got to spin up all the way to 4500rpm under no load. Now this isn't necessarily bad for the engine (ignoring the fact it's very uncomfortable for anyone in the car), but on a transversely mounted engine (e.g. in most FWD cars and in this case the Clio) it will play extra wear on your engine mounts, clutch, synchros. Again, this won't kill the car, but it will put extra wear on the above items.
By rev matching, you're just revving the engine whilst the clutch is down to match what the revs will be in the newly selected gear. So you're at 3k rpm in 3rd, you want 2nd, so you press the clutch, the revs start to drop, you 'blip' the throttle to as close to 4500 as you can and release the clutch. It will be smooth and put less wear on parts of the car.
Heal & Toe is just rev matching whilst braking, so you position the ball of your foot on the brake, and pivot the bottom of your foot onto the accelerator to achieve the blip. This is not only smooth, but it means you're already in the right gear to accelerate when you come off the brakes.