MySQL has it's own form of user authentication. It uses the tables in the mysql database to maintain user privileges. There are a couple different methods for adding users and specifying privileges. You really need to read this ...
http://www.mysql.com/doc/en/Privileges.html
If you are using MySQL from your ISP and your user does not have permission to GRANT permissions to other users, you may have to have the ISP add your users for you.