The Host opens a game and invites you. You take control over one of his main characters, now you can fight and explore the world with him or without him.
After you stopped playing you can somehow get the savegame of the host. Since its your friend, you can just ask him per steam-chat or whatever what he is playing right now.
For what do you need dedicated servers? Larian expects that 90% will play it solo. Coop is just for friends family or whatever. The game needs strategy you need to discuss it with your coop-partner its no ARPG like Diablo where you cant do anything wrong its a cRPG where you have to bear consequences for what your partner did.
