In a first season episode of Star Trek: The Next Generation called The Battle, we learn about the first command of Captain Jean-Luc Picard. He served on the USS Stargazer but lost his ship about nine years ago in The Battle of Maxia. The son of a Ferengi known as Daimon Bok was Picard's opponent back then, and his ship was crushed when Picard used a before unused tactical starship maneuver on Daimon Bok's son, surprising the hell out of him, crippling his ship, and killing Daimon Bok's son. Since that day, people in the United Federation of Planets refer to this battle tactic as The Picard Maneuver because it turned out to be so cool.

Daimon Bok finds the Stargazer, and offers to return it to the Captain as a token of appreciation between the two races. Needless to say that's not what the Ferengi has in mind. Ferengi never give anything away for free. In the episode The Battle, Daimon Bok tries to get revenge on Picard. He uses a brain scramble thingy that forces Picard to relive the events of that battle, and Picard almost uses his Picard maneuver on The Enterprise. But in the end Doctor Beverly Crusher saves the day and all is righted in the universe.

Anyway. The Picard Maneuver is a tactical battle move, in which the starship's warp engines are used in a risky but dramatic way, so that to the enemy it appears for just a few seconds that there are suddenly two ships attacking them instead of one. Since the badguys don't know which one to shoot at, this confuses the opponent and gives the attacker the edge.

Now. I told you that story to tell you this one.

During filming of the Star Trek Next Generation series, the actors would crack jokes and be generally silly to one another in between takes. Brent Spiner who played Data on the tv show and subsequent movies, noticed that every once in awhile Patrick Stewart did this weird little thing with his costume when he played the part of Picard. He'd take his hands, grab near the bottom front of the shirt, and tug down on it. It did give a bit of an air that the costume was more like a uniform, thus adding to the appearance of realism for this otherwise unreal futuristic show. One day when Spiner caught Stewart doing that, he called him on it, and laughingly referred to it as "The Picard Maneuver." Everybody got a good laugh at Stewart's expense, and as the urban legend goes, Stewart was a good sport about it all.

But it didn't stop there. If you watch the show at all, periodically you might notice many of the men working that bit of stage business into their performances. It's not done too much, but Spiner, Jonathan Frakes, LeVar Burton and even Michael Dorn did it at least once on the show throughout its seven season run. They'd grab the lower part of the top shirt and tug on it, thus performing the Picard Maneuver. Unfortunately I don't think Gates McFadden or Marina Sirtis ever did it. Chances are if they did, considering the photon torpedoes they were both sporting, they mighta fallen out of the suit.
Some ST fans made a list of other "maneuvers" for which other ST characters could be famous. A collection of them is available at http://startrek.miningco.com/tvradio/startrek/blmaneuver.htm Personally my favorite is the Chekhov Maneuver.