This is a football term defined as the area behind the line of scrimmage where the quarterback is protected from rushing defenders. It is more strictly defined as the area between the tackles. On the offensive line there are many offensive lineman, there are two tackles on each side of the quarterback (usually two linemen away from the center). The offensive line is tasked with protecting the quarterback so they have the time necessary to pass the ball to an open receiver.
The pocket is known as such because when a play begins, the area is typically rounded, with a buffer between the offensive line and the quarterback. If looked at from above, it appears as if the quarterback is in a "pocket" of protection behind the offensive line. If a quarterback leaves the pocket, they put themselves at risk of getting sacked.
Furthermore, if the quarterback is within the pocket and throws the ball away to avoid a sack, they may be called for intentional grounding if there is no receiver near where the ball is thrown. If the quarterback is outside of the pocket, no penalty will be called.