To view a database's tables and data, click "Manage" button. If phpMyAdmin is installed for this virtual server, you will also see a "Manage in phpMyAdmin" button. If the virtual server is a sub-server and it has its own phpMyAdmin install, that one is used instead of the parent's. If there is no per-server install, but a system default phpMyAdmin has been set, that shared instance will be used.
To see additional details about a database, including its size and number of tables, click its name.