The Tiger Driver is a powerbomb variation used most notably by Mitsuharu Misawa, though Dean Malenko, William Regal, and Ahmed Johnson have all been known to use it as well. The generic name for the Tiger Driver is the double underhook powerbomb. It got the name Tiger Driver because Misawa invented it when he wrestled as Tiger Mask.
For a Tiger Driver, the attacker sets up his victim in the standard powerbomb/piledriver position. The attacker then hooks both of his victim's arms behind (above) the victim's back. The attacker then pulls up on the arms, flipping the victim up and over into a powerbomb. For those familiar with WWE, HHH's Pedigree move is set up exactly like the Tiger Driver, except HHH simply drops to his knees, driving his opponent's face into the mat, rather than turning it into a powerbomb.
Misawa also created the Tiger Driver '91, a variation on the Tiger Driver. The Tiger Driver '91 is set up exactly like a standard Tiger Driver, except that the attacker keeps his victim's arms hooked during the execution of the move, forcefully driving his victim's head and shoulders to the mat, as opposed to the normal Tiger Driver where the victim lands on his back. The Tiger Driver '91 is typical of the particularly brutal "head-dropping" moves that All Japan Pro-Wrestling became known for in the mid to late 90's.
The Tiger Driver is considered a devastating move in Japan, and will frequently be followed by a successful pinfall.