MariaDB is a community-developed branch of the MySQL relational database management system.
MariaDB is intended to be a free, mostly backwards compatible drop-in replacement for MySQL.
It is a fork of Oracle's MySQL database and its initial release was kept up to date with the MySQL release of the same version. With MariaDB release 10.0 the developers team deliberately broke with the versioning scheme to make transparent there are some incompatibilities from there on.
See the MariaDB FAQ for more information and MariaDB versus MySQL - Compatibility for information on incompatibilities.
MariaDB home page