MySQL is a relational database management system that follows the Structured Query Language standard, it is released under Open Source License and widely used by web developers for building complex website applications.
Many popular open source programs like phpBB forums, PHPNuke CMS, OsCommerce Shopping Cart etc. are build with PHP scripting language and MySQL database.
There are many popular websites like digg.com
are built with PHP and storing data in MySQL backend too.
To know more about MySQL and learn indepth knowledge of using the SQL language for creating, storing and retrieving data from MySQL databases, you can check on the MySQL Official Website for complete Official MySQL documentation.
MySQL can run on Windows server and Linux servers, but many web developers prefer to have a Linux based implementation, or known as LAMP servers (Linux,Apache,MySQL,PHP) that claim to be much reliable and stable.