Music server

A server is a computer somewhere in a network. There is a program ( the server process) listening for clients. If the client ask for something, the server will start to do what the client  asked for (that’s serving).

A music server is a computer where the music is stored and has a process running which enables clients to browse its content and to stream selected songs to the client over the network.

Any computer with the appropriate software can do the job but often a NAS is preferred simply because it is a small computer so low on power consumption (you don't need much performance to stream audio).
The music server software is often UPnP compliant.

 

Music server is also used to label a specific type of computers.
They are what they are, a computer with a soundcard, but they do have the look of audio gear.