Servers are used to store webpages. A server does not
necessarily need to be a "special computer", either. I have a
computer at home that is always on (used as a TIVO box). This same
computer provides a webpage. The trick is you "need" a static IP to
run a web page - something you typically won't get without a T1
(minimum). You can use a service like dyndns to provide a pointer
to your computer to get around this.
A static IP is simply an IP that will not change. If you have a
webpage, you want people to be able to get to it; if your IP is
constantly subject to change, there's no guaruntee anyone can find
you.