The Wildcat formation describes a formation for the offense in football in which the ball is snapped not to the quarterback but directly to a player of another position lined up at the quarterback position. (In most systems, this is a running back, but some playbooks have the wide receiver) The Wildcat features an unbalanced offensive line and looks to the defense like a sweep behind zone blocking. A player moves across the formation prior to the snap. However, once this player crosses the position of the running back who will receive the snap, the play develops, unlike the sweep.
Here is a clip of the Bears using the Wildcat last year: