It means MyBB is trying to use a database type that your server does not support.
In ./inc/config.php, find $config['database']['type'] =
-> If it says mysqli, change it to mysql.
-> If it says mysql, change it to mysqli.
This is presuming you are using MySQL.
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).
Solution:
Open ./inc/config.php and check $config['database']['type'] is correct.
EDIT: Joshua