the mySQL server is to store cached mails taht RC downloads from the IMAP server. EMAILS ARE LEFT ON THE IMAP SERVER (unless deleted). RC uses mySQL to define it's user-base as well as store preferences and other such information on a per-user basis.
If you install RC on your server, make sure you have mySQL running and that's it. Edit the main.inc.php and the db.inc.php file and you're good to go.