Power shifting is a driving technique employed by drivers who wish to push the limits of their cars. Generally used in drag races to decrease the overall amount of time that it takes a car to travel one quarter mile. Power shifting is most effective for the 2nd to 3rd shift and the 3rd to 4th shift, depending on the number of gears your transmission has and how close they are (ratio wise).
To power shift you must have a manual transmission. After you've found a car with a manual transmission and assuming you've launched your car and are traveling at speed. Wait until the car's RPMs are nearing the redline then quickly depress the clutch and shift to the next gear as fast as possible without taking your foot off the gas. Note that you might not want to leave the gas floored but closer to half throttle, timing here is crucial. Once you have placed the transmission in the proper gear, dump the clutch and floor the gas again. If you wait too long to release the clutch your engine will over rev or hit the rev limiter (provided your car has one). This is a potentially dangerous maneuver as YOU CAN BLOW UP YOUR ENGINE if you miss the gear, rev the engine too high or for too long. If executed sucessfully your car will bolt ahead as your engine screams back into its power band.