NAS

Network Attached Storage is a computer connected to the network.

In the past its function was to store files.

Today it comes bundled with a lot more functionality.

Compared with a PC a NAS is:

lower on power consumption,
produces less noise (go for a fan less design id you really need a real quiet one)

This of couse depends strongly on the model.

Dropping prices makes RAID a affordable solution.

An alternative is remote replication (backup over the internet).

Functionality

This is the original use of a NAS. A cheap solution to to allow users to read/write/share files over the network.

They come in many flavours.

UPnP compliant multi media server.
Check user forums before you buy. A lot of these server software is very buggy and/or cracks under load. Mature products like TwonkyVision don't have these problems.
SqueezeCenter
A must if you use Squeezeboxes.
Check if it is possible to install SqueezeCenter.
Check the performance. SqueezeCenter has become quit big. 256 Mb RAM and a 500 Mhz processor is probably a minimum.
iTunes server.

Support for download through BitTorrent, FTP and HTTP

All you need to host your own website.

If your MP3 player can be used to make a phone call, why not let your NAS doing the ripping.