His style is often discussed in contrast with other French painters of the time who were more interested in drama, motion, movement and loose brushwork- they were the Romantics like Theodore Gericault. David's style is linear (as opposed to painterly) and his palette is cool; lighting is used to dramatically enhance his subject matter.
Jacques Louis-David was political and in favor of the Revolution in France, and used subjects from ancient history as references to the overthrow of other political tyrannies.