There's no single multiplayer world.
Each server hosts it's own world and when the players connect to that server they play that world. If they connect to a different server then they will play a different world. Your state in that world is saved so when you disconnect and reconnect you are restored to the same location with the same inventory items in your possession.
I don't know for sure, but I suspect that the data is saved on the server.
When you play you connect to the Mojang servers for authentication only.