It's a little more than a username and password. There's network access rules, user rules, auth rules, database and table control to the Nth degree. The mysql user doesn't need an account on the machine, just the proper priveleges granted to them by the database.
Spend a 1/2 hour or so reading the authentication/access parts of the documentation. You really need to make sure you understand this so that you don't leave a huge barn door open in your database access rules.