The Templar Order is a new faction to Diablo, and not much is known about them, currently. The follower Templar Kormac belongs to this order.
To quote Blizzard from the Follower FAQ[1]:
The Templar order is a new group that we're introducing as part of the Diablo universe; they have their own agenda, they're not paladins, and they have a different belief system and code of ethics that they follow.