Here's an article on it. Basically the pose was a recommended position for orators in ancient Greece, but a portrait of Napoleon by Jacques-Louis David was one of his best remembered image and a fad started. In 1738, Francois Nivelon, the Mr. Manners of that era, wrote in his book A Book Of Genteel Behavior that the hand-inside-vest pose signified “manly boldness tempered with modesty.” Originally the pose was to show the subject is well-bred and shows leadership yet remains humble. As with all trends there is no rhyme or reason anymore once it catches on.

Note that various myths often attribute this pose to things like the subject has cancer/ulcer/itching skin/deformed hand (why would you draw attention to it?) or painting hand was expensive (I doubt people like Napoleon or George Washington would be that cheap).