mojoPortal supports several different flavors of database, my guess is you are using the one from the web app gallery which is using Microsoft SQL Server. You can confirm it by going to Administration > System Information in your site.
Probably you installed the whole shebang with the platform installer or directly with WebMatrix and it installed all the needed dependencies such as SQL Server Express. The database for SQL server does exist on disk (usually somewhere under Programs Files/Microsoft SQL Server) but its not as simple as just copying a file to move a site and its data. You would need to copy all the web files up to the host, but for the database you would have to create a backup using the SQL Management Studio and then you would restore the backup on the host and may even need to get help from the hosting company because after restoring the database on a new server the sql user gets orphaned and has to be re-created or re-attached.
The Platform Installer may not have installed the SQL Express management tools but if not you should be able to go back into platform installer and install it.
I'm not all that familiar yet with WebMatrix, it may have tools built in for managing the database so you may be able to create a backup from there. It may have a way to publish the site and the database together, but I have a feeling you're going to need the help of someone more technical to move your site to hosting.
See also Moving an Installation of mojoPortal to a Different Server.
Hope it helps,