It's a proprietary movie format used with MP4 players and MP3 players with video capability.
When used in this way, though, it is an acronym that stands for "anime music video", and refers to anime video clips being compiled and put to a song (with the original audio of the anime stripped or blocked). However, as the acronym became highly used, it's meaning was lost, and people began to use it for anything done in that format, be it a movie, TV show, anime series, video game, whatever.