Simply stated, a play-action pass is a play in American Football in which the quarterback fakes a handoff to a running back before passing to a receiver. The play-action pass is one of the most common plays in football, such that some teams run it on virtually every passing play.
A successful play-action fake will draw the linebackers in, sometimes even causing them to pursue a running back who doesn't have the ball, or at the very least, cause them a moment's hesitation that could be the difference between a successful pass play and and an incompletion.
The play-action pass is obviously most effective when there is a reasonable expectation of a running play. Thus it is most often seen in clear running situations, and is most effectively used by teams that have a strong running game. Otherwise, the defense will completely ignore the play-action and focus on the receivers.
Although the play-action pass seems like an obvious call when a team plans to pass in what would normally be a running situation, the play is not without some risk. Play-action requires a few precious seconds to execute, and thus depends on good pass protection from the offensive line to avoid a sack or a hurried pass. It also requires effective timing between the quarterback and the running back to sell it to the defense, and of course, any time the quarterback does anything with the ball other than holding it tightly in both hands, there is an increased risk of a fumble.
The opposite of a play-action pass would be a play that fakes a pass and then runs the ball instead, such as a delayed handoff or a quarterback draw. A similar (although much more risky) play to the play-action pass would be the flea-flicker.