Basically, another world is invading ours. The other world, named Thule, was once a part of Atlantis. But when King Atlan succeeded in uniting Atlantis, a sect of wizards escaped by creating their own world. But now whatever magic kept them apart is failing. But they knew this day would come and so have spent centuries preparing for it, with the intent of conquering our world.
Arthur went to fight this threat on his own, leaving Mera behind as Queen of Atlantis. But when he came back to tell her that there are many innocent people who would be killed if he outright destroyed Thule, she accused him of being a traitor. So Arthur has been been trying to rescue the innocent Atlanteans of Thule while fighting the dark magics of the wizard kings AND evading the team Mera has sent to capture him.
Of course, Mera isn't actually Mera; her shapeshifter sister has taken her place on the throne. I was thinking she'd been mind controlled or something because the angry Mera on the throne was obviously not the regular Mera.
So Arthur fights everyone on his own for awhile until Wonder Woman confronts him. Then he gets the rest of the Justice League to help him invade Thule and destroy it while making sure as many innocents as possible get out. Oh yeah and he takes a little time out before this to go save Mera (but it's ok, she manages to save herself in the meantime - Mera is awesome!)
So while confusing at first, overall Exiled is a pretty good read. Still no war of the Seven Seas though (which was totally alluded to at the end of Volume 4). But apparently there's a Volume 8 coming, so *maybe* it'll be in there?