DivX stands for Digital Video Xtreme.
It is known as a video codec which has good compression ratios while preserving a good quality based on the H.263 codec. It is closed source.
When DivX Inc. introduced the DivX6 format DivX became a container, too. The file extension for the DivX container is .divx (Still under development) but normally the DivX encoded video will reside inside an AVI container.