An Acronym (almost?) for MPEG 1 layer 3.
MPEG stands for motion pictures expert group, and it refers to a family of standards for displaying video and audio - normally using lossy compression. MP3 is one of the methods that can be used for encoding the audio, and has become vastly popular.
MP3 uses lossy compression to remove frequencies that are "masked". Some of the algorithms used in it are patented by Thompson and Fraunhofer IIS. They say that only commercial users (ie software and hardware sellers) have to license it - players that are given away for free do not have to be licensed. However, this is also what Unisys said about the LZW patent...
A free, alternative format is OggVorbis.