Commonly referred to as a heel-toe downshift, a blipshift is a technique used in manual transmission driving to smoothly downshift gears while braking. It consists of using your left foot to operate the clutch, braking with the toe of your right foot, and giving the gas pedal a small blip to match the engine speed with the transmission and wheels' speed. This can be done in conjunction with or without double clutching as per the driver's and gearbox's preference.
Before downshifting, the RPM in the new gear will be higher than the RPM your engine is currently spinning, necessitating a blip of the gas to match up the revs or a slipping of the clutch until the engine speed matches that of the wheels turning in the new, lower gear. Slipping of the clutch provides premature wear of the clutch and takes longer for the downshift to be completed. The amount of throttle needed for the blip depends on the spacing of the gear ratios and current RPM. Executing this technique smoothly takes skill and shows excellence in manual transmission driving ability.
Mastering the art of a blipshift makes you totally more awesomer.