Minor civs are just minor civs. They have no restrictions like the barb team, but cannot make diplomatic actions like the regular civs. Thus they can't contact and once you try to enter their states, it's all out war to the end of the game. Interestingly, you can bribe AI off them, but you can do zilch with minor civs.
They were created to represent minor nations that never went full-fledged. I don't know the first instance of their arrival, but I played Vanilla Greek World scenario made by Rhye. Extensively. And I think minor nations were created for representing something between disorganized barbarians and full-fledged nations...like the Celts.