FFmpeg is a collection of free software that can record, convert and stream digital audio and video. It includes libavcodec (a leading audio/video codec library), and libavformat (a leading audio/video container mux and demux library). FFmpeg is developed under Linux, but it can be compiled under most operating systems, including Windows.
Mythtv uses FFmpeg libraries Libavcodec, libavformat, and libavutil for its AV processing & displaying code, for example the internal player. Myth also provides mythffmpeg, a version of ffmpeg using the libraries as built for Myth.
Due to political reasons that first surfaced in the beginning of 2011, the FFmpeg project has now split into two independent forks: FFmpeg and Libav. As of 0.25, MythTV's internal copy of FFmpeg is from before the split.