As markkuk said, MySQL and system users are completely separate, see the links above for how to create a new user for your PHP application.
I wouldn't recommend using the root user incase your app has any vulnerabilities, create a restricted user that only has access to the databases/tables that it needs.
If your not comfortable using the mysql command line, have a look for "MySQL Administrator" and "MySQL Query Browser" on the mysql site. Not sure if they're available on Linux (I'd guess at yes), but they provide a nice click-through GUI to setup users and databases/tables.
to download them