You can put your media files on a NAS. You then need to run Media Centre on a computer, which could be a Pi, a desktop, a laptop or one of some other options. We'll call this the server.
Through Media Centre, you then create a library of the files on the NAS and manage them from that computer.
If you want to play your media from the server with another instance of MC on another device (a client) you load the server library on the second instance.
If you want to do things like edit cover art, edit tags, manage playlists, etc, from the second instance, you need to set up authentication on the server and log on when you load the library on the client.
If you want to do things like move or copy files on the NAS using the client instance of MC then you need to ensure that the path to the files on the NAS is the same for the client and the server and that the user on the client has the correct rights on the NAS.