A quarterback sneak in football is a play in which the quarterback of a team takes the snap from the center and immediately ducks forward into the offensive line in an attempt to gain a few yards. The quarterback sneak is used in situations where only a few yards are required for a first down or a touchdown, since that's all a quarterback will likely gain.
The goal of a quarterback sneak is to gain a few yards in order to convert a first down or a touchdown. The quarterback sneak is only run in situations when only a few yards are needed, as the play is very unlikely to get more than just a couple of yards. After the center snaps the ball, the quarterback tries to literally "sneak" a few yards forward before any defenders can get a hand on him.
The defensive strategy for stopping the quarterback sneak is to clog up the offense line with multiple defenders and force the quarterback to take a different route forward, which would allow a defender to possibly tackle them for a loss elsewhere. Or, the defense, can put so many players in the middle that the quarterback can't gain any yards.
The quarterback sneak can add a few points to a team's score, but it can be a bit risky. The quarterback is the most important player on the team, so it's vital to keep him in safe game scenarios. Making a quick gain of a few yards and getting tackled by defenders is risky for the quarterback's health and safety. This is why they are only performed in certain critical scenarios, where the course of the game could change entirely if it's successful.
The New England Patriots are often the team that is thought of when discussing quarterback sneaks. From 2001 to 2016, the Patriots attempted approximately double the league average amount of quarterback sneaks on short yardage plays. Patriots' quarterback Tom Brady is particularly good at quarterback sneaks.
Quarterback sneaks have been used much less in recent years. Teams have been opting to try passing plays instead on plays where they need to pick up one or two yards.