DivX : Basically, you copy the DVD's contents onto a hard drive, which is usually a couple of gigs. In a nutshell, you use a program, and you convert the DVDs contents into an avi file. DivX is what the encoding for the avi file is called (it's different from other avi files). i think it's also called MPEG-4, with 1 and 2 being video (i think), 3 being audio, and this being the newest incarnation of the mpeg family.
Now, DivX does not necessairily mean it's a DVD rip. DVD rips can also be converted to MPEG format, for use in Home Theater DVD players, so you can watch it on TV. Those are usually called VCDs (short for Video CD, the format that the movie is burned on the CD, basically the MPEG and files on the CD). There are others, like SVCD, which provides higher picture quality, but is somewhat lacking on most DVD players. You can't watch a DivX movie on a DVD player, unless there is some super new player that plays VCDs.
Also, Divx doesn't mean it's a DVD movie. The encoding can be used for any video, so it can be used for porn (not that i'd know...), home movies, etc.