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Powershifting is the act of switching out and quickly or instantly (only a puff of smoke visible) back into Cat Form or Bear Form as a Druid with the Furor Talent to gain an instant boost of Rage or Energy.
This was an advanced technique used by many skilled or knowledgeable feral dps players in The Burning Crusade while chain-drinking Mana Potions (!) in order to squeeze out as much energy and therefore dps as possible. It was also sometimes used in conjunction with the infamous level 40 (!) Wolfshead Helm which caused the strange appearance of very highly-geared Feral Druids raiding in fully epic tier sets and the latest, best gear - but still using a Rare helm normally crafted using simple materials for characters not even level 60.
A furor combined with Wolfshead Helm powershift was worth 1 full shred and 1⁄3 the cost of another shred. Meaning each powershift granted an ability that caused 293% more damage and 527 bonus damage that would not have been available without the powershift.
This technique was nerfed in Patch ___ by a change to the Furor Talent toward the end of The Burning Crusade and will not return, according to Blizzard posters on the Official Forums - as it was never intended and caused some rather strange player behaviour.
The name comes from the real-life motor racing term which refers to "The clutch [being] briefly depressed while the shift lever is slammed from gear to gear, keeping the engine in its power band." See the Wikipedia article on Powershifting.