Cutoff Seat is the seat before the dealer. The dealer is represented by the dealer button that is placed in front of him and the players take turns being the dealer each hand by moving the dealer button clockwise. The Cutoff Seat is therefore the player that acts right before the dealer.
Recently, the cutoff seat has become a popular topic of discussion in No Limit Texas Holdem because of the regularity with which players not try to steal the blinds from the cutoff seat instead of the more traditional blind stealing position of the dealer.