While you can host a multiplayer game with the game launched, a dedicated server allows much more functionality, and makes it possible for someone to leave the server running for others to play on without leaving yourself in the game idle.

I found a website with a slew of downloadable content for XIII and dedicated server software.

Here's a link:
http://xiii.opaquit.com/downloads.php

This site hosts a number of useful files that one might get a kick out of if you're enjoying XIII.