Open ./inc/config.php and check $config['database']['type'] is correct.
This means that the database extension your forum was running on has been disabled.
Check ./inc/config.php to see if the database type is set correctly and that it is available to use on your server. If you're not sure, ask your host which one you should be using (mySQL, mySQLi, pgSQL or SQLite).
What AJS and Tom said. It could be however that your host disabled all DB Extensions on whatever package you use.