Sneaking is movement into enemy provinces without being detected. Only Stealthy units can attempt such moves. Their chance of success (and of staying hidden in an enemy province once they are there) depends on their Stealthy rating, the number of units trying to hide, and the number of units looking for them.
Provincial defense automatically searches for hidden units in its province each turn as long as the defense level is 15 or greater. A commander, however, must be set to the Patrol order. Fast units, like cavalry, or units which fly, are better at revealing hidden units than slow units or non-flying units are. Units with a Patrol bonus are also better, as you might expect. Units may also Sneak and attack, which allows stealthy units hiding in an enemy province to attack an adjacent enemy province. Combat will not occur unless the unit is discovered by patrollers or other means. This is the default move for stealthy units.
To give a stealthy commander the order to move normally and thus attack the province it enters), hold down [Ctrl] while left-clicking on the destination province. A stealthy commander will not sneak unless all units under his or her command are stealthy as well. Removing non-stealthy units from the commander will not automatically change his move back to sneak.