“i” in mysqli stands for “improved” so in short mysqli is a improved version of MySQL with following advantages -
Object-oriented interface: You can still use the "old procedural" way of calling the mysql extension but the OO version groups the functions by their purpose.
Prepared Statements: Those are useful to prevent SQL injections and are executed faster.
Multiple Statements: With this "feature", you can execute multiple SQL queries inside only one "mysqli" call. This reduces the round trips between the database server and the PHP server.
Support for Transactions: This is really useful to write robust applications. It gives you the ability to write a group of SQL statements that will either be executed or all rolled back (usually if there is an error somewhere in the process).
Enhanced debugging capabilities: As an example, you can use "mysqli_debug(...)" to save debugging information into a file.
Embedded server support: Since MySQL 4.0, there is a library available that can be used to run a complete MySQL server embedded inside a program, usually a desktop application.