An offensive (trick) play that involves the running back taking a hand-off, then throwing a backwards pass back to the quarterback, followed by the quarterback making a forward pass to an open receiver.
The play was created by Bob Zuppke in 1910. In the 1967 book Football Lingo Zuppke said the phrase intended to "evoke the quick, flicking action of a dog getting rid of fleas".
A flea flicker is designed to trick the defensive players into thinking it's a running play which can result in receivers or a tight end being wide open. It's thought to be a high-risk/high-reward play because it often results in either a long pass completion, sack, or turnover.
In football the quarterback usually has mere seconds to throw the ball before defending players are in his face. Performing a flea flicker involves a handoff, lateral, then the quarterback planting his feet and throwing...therefore the offensive line must do an impecable protection job.