MySQL is an open source relational database management system (RDBMS) that can be easily implemented and managed either on-premise or via the cloud through a hosting provider. It supports lots of simultaneous writes and scales via replication (though this can get complicated). For this reason and because of its relatively low maintenance/scalability costs, it is primarily used as a production database.
Created in 1994, MySQL is one of the best-established RDBMSs and has evolved significantly since then. Ninety percent of websites use MySQL. These include giant services like Youtube, Twitter, Wikipedia and Facebook.