Genshin Impact co-op mode

I really love this game and I'm super addicted. 

I don't quite understand co-op mode. I guess it automatically activates when you open the game. I usually forget and don't notice until people start requesting to join my world. I let them join but then I lose track of my quests. It seems that you can't do most of the quests with another player. Sometimes they try and chat me too but I have no idea how to respond. I'm on ps5 and I read that you must press the center button and square or X and the keyboard will some up. That does nothing for me. So what is the point of co-op mode, really? I just don't understand yet. Sorry if I sound like a newb. I'd just like to learn if it's useful or not.