It's one of the final levels you need to beat to unlock "True Enthusiast Power": the heel-toe downshift.
This is a perplexing bit of coordination that, once you perfect it, truly makes you feel like an actual master. Until then, you're stuck hoping that your quick rev-matching blipshift is enough to do the trick and get you around a corner smoothly. It might—but it also might cause the smell of burning clutch to fill your nose.
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Engineering Explained is here to help make sure you're not only pulling off the heel-toe downshift correctly, but also to show you exactly what's going on behind the scenes when you heel-toe downshift.
The heel-toe downshift is a means to slow your car as you enter a corner and get yourself into the proper gear for smooth, fast acceleration out of a turn. This means you'll need to hit the brake, clutch, and gas while also shifting down a gear or two.
Now, I know you don't have three feet so how do you manage to hit all three pedals at once? Brake with your right foot. Clutch in with your left foot. With your right foot still on the brake, roll the other half of that foot on to the gas or slide your heel over if the pedals are spaced far apart and blip the throttle to bring the revs up. Now you can downshift properly and keep your car balanced.
Release the brake, apply more throttle, and accelerate away from the turn like a boss. You've just completed a proper heel-toe downshift. Now go find a curvy road and practice that until you can do it smoothly every time.