Some people might say "If you really have to ask, then it's not for you."
But a server can give you a bunch of stuff:
-Network accounts. This would allow you to log into any of your computers (as long as it's on the same network) and access all your files.
-Calendar server. I don't know if you have a Gmail account, but it's like Google Calendar. You can store all your calendar information there. Plus, each user you have (say you, your spouse, and kids if you have any) can each have their own.
-E-Mail server. Self-explanatory.
-Web server
So it depends on what you need.