Almost everything entered by you in the administration panel of your site is stored in the MySQL database for your website: post title and content, metadata about authors and publishing dates, the categories and tags attached to a post, users registered on the site, all of the settings on the site, and so on.
When you load a page on your WordPress site, the code in WordPress itself, the active theme and your active plugins communicate with your MySQL database which responds with the information requested. That information is then inserted into the web page generated by WordPress, which is sent to the browser and displayed to the visitor.
Like WordPress itself, MySQL is released as open source under the GNU General Public License. MySQL was created by the Swedish company MySQL AB in 1995. In 2008, Sun Microsystems bought MySQL for $1 billion, and in April 2009, Sun was in turn acquired by Oracle Corporation. Oracle remains the primary developer of MySQL to this day, and offer both a free version and a premium one with additional functionality.