MySQL is one of the supported databases that underpins a Moodle installation.
MySQL describes itself thus:
"MySQL, the most popular Open Source SQL database management system, is developed, distributed, and supported by MySQL AB. MySQL AB is a commercial company, founded by the MySQL developers. It is a second generation Open Source company that unites Open Source values and methodology with a successful business model.
The MySQL Web site (http://www.mysql.com/) provides the latest information about MySQL software and MySQL AB."