Power shifting is only applied to automatic transmissions. In standards, it's basically just pushing the car past optimum shifting range.

In automatics, you have the ability of using your base, or power, gears instead of letting automatic shifting to higher gears. These are usually gears 1-3. Because manual transmissions can be pushed further, they have a tendency to be faster, when compared to automatics. Say you are driving at a constant 30 mph. Another car pulls beside, hinting at a race. Reach down to your gear shift, and move the shifter from D to 3. (This is if your power gears are 2 and 3). At the same time, step a little harder on the gas. As the car shifts into the lower gear, the torque increases, causing the car hop forward in speed. Once your RPMs reach 5000, shift back into drive. By this time, you should have a great deal of speed built up.

This only works if you have a powerful engine. If you are thinking of racing that 79 Firebird in your Honda Accord, you may want to reconsider. : )