MySQL was developed by Swedish firm TcX, in 1996. They created it because they needed a relational database which could handle large amounts of data on relatively cheap hardware.
Nothing out there could provide what they needed, so they created it themselves, bless 'em. MySQL is the fastest relational database on the market. It outperforms all the leading databases in almost every category. It has virtually all the functionality that the other leading databases have, but it costs bugger all!
MySQL has increased in popularity since 1999, largely due to the success of Linux and the rest of the Open Source movement.