The wildcat formation in football is a formation similar to the shotgun formation, but a player other than the quarterback, usually a wide receiver or running back, takes the snap. Wildcat was created for confusing defenses and placing a good runner at the quarterback position, and it occasionally works.
Wildcat often relies on using a number of misdirection tactics, including motions before the play, read options, and draws. Wildcat typically puts the best runners in the backfield and makes the defense spread themselves thin. For example, a wildcat play that includes a jet motion forces the defense to be wary of an outside run, but the wildcat QB is still a threat for a backside run. This forces the defense to leave an end watching the backside, but often the linebackers will shift for the motion, creating a gap up the middle of the play for the quarterback to run a draw through. The idea is that wildcat forces the defense to respect every threat.
Some wildcat offenses have shown versatility in offering pass plays. An example of this is the Philadelphia Eagles' trick play against the New England Patriots in Super Bowl LII. The play, referred to as the "Philly Special", was run in a 4th and goal situation and saw running back Corey Clement take the snap, then pitch to tight end Trey Burton on a supposed reverse. Rather than run the ball, however, Burton passed the ball to quarterback Nick Foles who successfully caught the pass for a touchdown. Many other wildcat passes exist that rely on less intricate play design, but the central theme of misdirection remains.
Wildcat is a pretty novel formation all things considered. It's easily countered by a good disciplined defense. Realistically, most teams won't run the wildcat offense for a prolonged period of time unless their quarterback is terrible. The last team that notably ran a considerable amount of wildcat was the 2008 Miami Dolphins. While the formation saw early success, it's prolonged overuse allowed other team's defense to adequately prepare. This is true at any level. Effectively, if a defense wants to stop a wildcat offense, they simply have to be prepared for it to occur like any other trick play.