Short answers, pulled from the story.
The hand-in-waistcoat gesture required speakers to keep one hand concealed within their garment while addressing an audience. In the 4th century before Christ, Aeschines taught rhetoric at a school in Athens where he instructed students that speaking with an arm outside of their chiton was considered bad manners.
Jacques-Louis David painted Napoleon Bonaparte in His Study in 1812. The Emperor stands inside his Tuileries palace study with his right hand inserted into his waistcoat and this specific painting made the pose famous across Europe and America.
Art historian Arline Meyer argued that the pose became a visualization of English national character as a visual counterpoint to perceived French excesses during times of political tension. Critics contrasted this stance with the gestural exuberance of the French rhetorical style which they viewed as having Catholic and absolutist associations.
Mid-19th century photography adopted the tradition for both aesthetic and technical reasons because photographers encouraged sitters to place their hand inside their jacket to prevent blurring. Maintaining the sitter's hand in a single place reduced motion blur during long exposure times used for daguerreotypes or ambrotypes.
The gesture is known to Freemasons who incorporate it into specific rituals and symbols. Members of the military frequently appear in photographs with their right hand inserted into their waistcoat and the stance appears in portraits where three open buttons on a tunic suggest the concealed hand.