An open source MPEG-4 video codec project which was launched in 2001 to continue Project Mayo's open source DivX codec.
Basically a short piece of history is required in here to understand this fully.
Original DivX ;-) codec was not developed from the scratch, but was just a hacked version of Microsoft's WMV video codec. This version, best known as DivX ;-) v3.11 alpha (which was the last official version of the hacked codec), quickly became ridiculously popular among videofreaks all over the world.
After its success, group of people, most notably the hacker behind the DivX ;-) codec, started developing a legal version of the codec which would be a real codec instead of basic hack of existing Microsoft codec.
They launched an open source project, dubbed as Project Mayo (also known as OpenDivX) to develop this codec. After a while the codec matured, but the original developers wanted to push it further and started a company called DivXNetworks which started developing its own closed source version, based on the work of the Project Mayo. Eventually this closed source codec was released as DivX 4 (since then, we've seen this closed source version to develop further and currently, 09/2005, the latest version of the codec is called DivX 6.0).
Now, open source guys didn't want to abandon the work of the Project Mayo and they continued to develop the codec further and the XviD was born.
XviD, like many other MPEG-4 formats, can be played with certain MPEG-4 compatible, stand-alone DVD/DivX/XviD players.