Firefox vendors a subset of ffmpeg, to decode royalty free codecs such as vp8/9, mp3, flac, on all OSes. We're using our own decoders/demuxers for other royalty free codecs for historical reasons.
It can also use the system's ffmpeg to decode patented formats such as h264 or AAC, on desktop Linux, if the copy of ffmpeg present on the host includes non-free codecs (same on other OSes, with their respective system libraries).