The "i" stands for the "improved". The list of improvements of it can be found here.
MySQLi is the OOP version of the MySQL extension. In the result, MySQLi and MySQL achieve the same thing: they are extensions for interacting with the MySQL from PHP. Many people still use the original MySQL extension instead of the new MySQLi extension because MySQLi requires MySQL 4.1.13+ and PHP 5.0.7+.
MySQLi supports some things that the old MySQL extension doesn't support. Some things like the prepared statements, multiple statements, and transactions on top of my head.
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