From Online Manual
During your upgrade to SMF 2.1, MySQL users will see a check box to change over to MySQLi Functionality.
MySQLi is an improved version of the MySQL API interface in PHP. The PHP development team has decided to discontinue support for MySQL API extension in future versions of PHP. As of PHP 5.5, MySQL API functions will give a deprecated error on their usage. SMF automatically handles those messages, but the API will not exist forever and will be removed from PHP in future versions of SMF. In order to combat this, SMF 2.1 is compatible with MySQLi API, which provides similar functionality that MySQL API functions. As well provides access to new features offered in more recent versions of MySQL.
By default this option is checked. Although still in development, SMF 2.1 is being tested to support MySQLi and all its functionality with native SMF functions. We encourage this option to be used unless specific reasons such as hosts not supporting MySQLi are found. MySQL and MySQLi have similar functionality, can access the same database and can easily be switched between by modifying Settings.php and changing $db_type to 'mysqli'.