I'm not a number, I'm a free object!
The peer that has authority of a game object owns it and have the ability to update the state of an object. The state will then have to be replicated out to the other peers so they see they object state as being the same. Other peers that wish to change to object need to send the changes they wish to perform to the owner and then they will get the replicated changes back.
In a authoritative system every object in the game is owned by a peer that is called the server. The other peers, the clients send the actions they wish to perform to the server.
In a distributed system any peer can be the owner of an object.
Peers create proxy objects that can handle custom network messages.