When logged into cPanel, most users can simply click on the PHPMyAdmin icon to directly access their MySQL databases. Sometimes, however, the user is taken to the PHPMyAdmin login screen again, where they are prompted to enter a username and password.
A recent change in cPanel (since 11.28) has resulted in the MySQL root password NO LONGER being synchronized with the cPanel account password. If you change your cPanel password for any reason, this means the stored, MySQL root password for your account will be different. If you are not automatically logged into PHPMyAdmin, but instead are taken to the PHPMyAdmin login screen, it is because your cPanel account password has been changed, and the MySQL account password has not been updated automatically to reflect that.