It is what you do when you "heel-toe" shift. When you go from say 3rd gear to 2nd gear, you may be at 3000rpm in 3rd, but in 2nd you would be at 4500rpm, it will blip, or briefly rev the motor to about 5000rpm while the clutch is dis-engaged, and it will spin down to 4500 as it re-engages the clutch.
I'm not sure what the benefits are on modern full synchro transmissions, but it was essential on older transmissions, especially when shifting quickly. I think its mainly for racing situations, where you are at or near the performance capabilities, and maintaining traction under braking. This prevents sudden grabs and instability.
... plus it sounds cool.
Although I should note that heel-toeing also involves using the brake at the same time... Three pedals, two feet, and a lot of 'fun' to master.