The Picard Maneuver is a battle tactic invented by Starfleet Captain Jean-Luc Picard. In 2355, Picard was in command of the USS Stargazer when it was attacked by an unknown alien vessel, later determined to be of Ferengi origin. The subsequent engagement and destruction of the Ferengi ship was sometimes called the Battle of Maxia by some Ferengi.
The Picard Maneuver was born out of desperation during the battle. The Stargazer, which was damaged, suddenly accelerated into high warp directly towards the Ferengi ship. By doing so the Stargazer appeared to ship's sensors, for an instant, to be in two places at once. When data from the newly-moved ship reached the Ferengi ship's sensors, data from its previous position was still arriving, so the Ferengi effectively "saw" two Stargazers in different locations.
The conflicting and rapidly shifting data caused the Ferengi to target and fire on the wrong vessel, and since the Stargazer opened fire as soon as it dropped out of warp, the Ferengi ship had no time to maneuver out of the way before the phasers and photon torpedoes hit. The Ferengi ship was destroyed. This technique was so successful that it was named after Picard, and there was no known defense against it until 2364.
In 2364, Lieutenant Commander Data calculated a defense to the Picard Maneuver. He theorized that since space contains trace gases, active scanning close by for gaseous compression could serve as an indicator for the actual location of a ship that had just used the Picard Maneuver. This defense was first successfully used when Picard attempted to use the Picard Maneuver against the USS Enterprise-D while under the control of a thought maker deployed by DaiMon Bok.
Behind the scenes, it became common practice to refer to Patrick Stewart's habit of tugging his uniform shirt down when standing up as the "Picard Maneuver" (Star Trek: The Next Generation Companion).