The Barbarian is a heavy unit of the Early Middle Ages. It cannot be controlled by players, and is encounted on the campaign map in three bonus provinces- Galgenschlucht, Todespass and Steilsturz. It has ability Last Stand, which gains attack and defense bonus for every allied unit with Last Stand that is killed. When these units with last stand ability are killed, every remaining unit with Last Stand will be stronger. It also gains bonus on rocks and has a unit bonus vs light units, but is still vulnerable to both ranged and artillery units. In a battle it looks like a Berserker.
The best way to fight barbarians is to use their low defense to your advantage. Use Mounted Archers and Catapults to bring them health down (but don't kill them). Once their turn is passed to yours use your ranged units to pick them off one by one until none are left. This allows you to easily complete the provinces with EMA units.