This is normal.
In a basic standard mysql installation, you normally have the "mysql" database present and a "test" database. The test dbase can be deleted as far as i know.
The mysql database however can only be seen by the system mysqladmin or root. You should normally never use these accounts to login to phpmyadmin for security reasons.
But you -never- must delete the "mysql" database you discovered, that's the system databae containing the mysql admin password, amongst others.
That database is needed for the correct working of mysql.
So yes, this is normal, leave it there.