You might have thousands of tracks you've ripped from CD over the years, for example. This is the more conventional way to use iTunes and it's great, until your library starts to get too big for your hard drive. And with more and more people using ultraportable MacBook Airs, storage capacity can be an issue.
Luckily, iTunes makes it fairly easy to move your library to an external drive, even one connected to your Wi-Fi router. This can be a regular USB drive, for which you're best off using an Apple AirPort Extreme router, or a NAS (network attached storage) drive. These have special abilities, like being able to broadcast a music collection to any copies of iTunes on your network.
The clever thing about using iTunes Server on a NAS is that these drives tend to be very high capacity, and can be shared between lots of users. The beauty of having a shared, wireless music library is that it can be much bigger than one you would store on your Mac, and more advanced users can control who accesses it by tweaking the shared drive settings.
At a simpler level, you might just want to access the library yourself, in which case all you need is an AirPort Extreme and a USB hard drive.