DivX ;-) was developed by bunch of hackers, most notably a guy called gej and it is based on Microsoft's version of MPEG-4 encoding technology, called as Windows Media Video V3.
Basically Microsoft's encoders didn't allow users to save MPEG-4 streams into AVI structure format, but forced users to use ASF instead. It also had some other limitations -- and those limitations were overriden in DivX ;-). It also added a support for other than Windows Media Audio audio encoding technology, allowing users to have MP3 audio on their movies.
In 2001, original "developers" of this hacked (and therefor illegal) codec released a new legal version of DivX ;-), called DivX (without smiley). DivX (without smiley) supports old DivX ;-) movies and also adds new features and better compression quality than "original" DivX ;-).
The name, DivX ;-), comes from now defunct CircuitCity pay-per-view DVD format called DIVX.
With DivX ;-), you can store 50-120 minutes of relatively good quality video to one CD (740MB) (==most of the movies can be stored in one CD, unlike in VCD or SVCD). Only negative aspect DivX ;-) has when it's compared to VCD is the fact that VCDs can be played with regular stand-alone DVD players and DivXs can't.
DivX, like many other MPEG-4 formats, can however be played with certain MPEG-4 compatible, stand-alone DVD/DivX players.