A file with the extension .divx has been encoded with the DivX codec. DivX is an MPEG-4 format, therefore usually producing high quality video files at lower birates, especially from a DVD source. Most files encoded with DivX nowadays have a .avi extension but there are still plenty of .divx files floating around P2P networks.
You need to download and install the DivX codec to play back these files.
Related software tools
The latest version of the DivX. That is, you need to have this file installed if you want to watch DivX movies. And latest codec gives you the best quality.
DivX Pro (Win98/ME) (Shareware)
DivX is an extremely popular implementation of the MPEG-4 standard.