No, he didn’t have a stomach ulcer, or breast cancer, or a deformed hand, as some have theorized. Just like low-slung jeans and pet rocks, posing with one hand hidden was a fad that was considered a symbol of good breeding.
In his essay "Re-Dressing Classical Statuary: The Eighteenth-Century 'Hand-in-Waistcoat' Portrait," Arline Meyer notes that the pose dates back to Ancient Greece, when the hand-tucked-into-the-tunic stance was the recommended pose for orators. The post was used with "relentless frequency in England in the 18th century," Meyers writes, so much that the pose became a cliché—some portrait artists were actually accused of using it because they didn’t know how to paint hands.
But, Meyer says, "in real life, the 'hand-held-in' was a common stance for men of breeding." 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.”
Today, the "hand-in" pose is associated with Napoleon, thanks in part to Jacques-Louis David's 1812 painting, Napoleon in His Study (which Napoleon didn't sit for, but was commissioned for a Scottish nobleman)—what Meyers calls the gesture's "personalized revival in the nineteenth century":
It is not surprising that when Napoleon's reputation plummeted, a subtly arched postural inflection made the gesture decidedly imperious... The enduring French association is in fact somewhat ironic, in that the gesture had a voguish run as an English portrait convention long before it became Napoleon's quasi-military emblem.