MariaDB is a MySQL fork that is developed and maintained by original mySQL developers. It is considered to be more open and is being distributed as default MySQL compatible database by majority of modern linux distributions.
MariaDB is a drop-in replacement, you can use it with any stable supported Moodle version using standard mysql drivers. Since Moodle 2.6 there is a dedicated driver for MariaDB.
See MySQL for more information, the setup procedure is nearly identical.