MariaDB is a fork of the MySQL database project that provides a drop-in replacement for MySQL. It preserves API/ABI compatibility with MySQL and adds some new features.
The original company behind MySQL, MySQL AB, were bought out by Sun which was then bought by Oracle. Recent changes made by Oracle indicate they are moving the MySQL project to be more closed. They are no longer publishing any useful information about security issues (CVEs), and they are not providing complete regression tests any more, and a very large fraction of the mysql bug database is now not public.
MariaDB, which was founded by some of the original MySQL developers, has a more open-source attitude and an active community. We have found them to be much easier to work with, especially in regards to security matters.
MariaDB is default MySQL implementation in Fedora since Fedora 19 and was accepted on the base of this feature page.