Randomly encountering other people online during certain sections of the game. Not an MMO but kind of like Journey, but if you leave the map you won't see them again. Of course, they'll be registered on PSS.
For example, when you leave a town you usually have to go into this one small room and then exit out to the route, and while you're in it you might see a random person online. Could be the same for pokemon centers. You can communicate, trade, battle or do other stuff with them. It'll only randomly connect with someone whos party level and progress is around the same as yours.