ffmpeg and ffmpeg2theora are video converters used by Islandora to perform conversion and playback of different video types. The ffmpeg tool itself is a shell that can be set up to support different video and audio codecs, depending on the needs of the Islandora installation. ffmpeg2Theora is used to add functionality to ffmpeg, particularly in creating an OGG Vorbis copy of the video's audio stream. The installation process for these tools will vary deeply depending on the needs of your site.
ffmpeg is found on the official ffmpeg site's download page, http://ffmpeg.org/download.html
ffmpeg2theora is found at http://v2v.cc/~j/ffmpeg2theora/download.html
ffmpeg's downloads page includes links to its source code for installation; however, in order for Islandora to support additional codecs, additional libraries will have to be installed and enabled during compilation. For additional information, check ffmpeg's compilation guide on how to include additional codecs for your operating system and compile ffmpeg.
ffmpeg2Theora's downloads page includes both the source code and binaries for installation; you may be able to install from the binaries, or for Linux installations, ffmpeg2Theora may be included in your distribution's package manager. For Debian- or Ubuntu-based systems, you can use:
sudo apt-get install ffmpeg2theora
Check the configuration section for the Video Solution Pack for more information on how to integrate these converters into Islandora.