What are they?  Procedures change for these?  I tried looking it up, and FAA.gov gives a list but not an explanation for them.  Just a wonderin'

i believe it has to do with ILS landings, and minimums for a safe landing. also i think maybe to do with auto landings.
but i will let someone add all the details

For the sake of simplicity, a CAT II or III ILS is the exact same thing as a CAT I, except that the decision height is lower. If you have a CAT II or III approach plate, you can fly it to 200' AGL just like any other ILS. This is where it gets complicated. You might want to find a copy of FLY THE WING which is an excellent book by the way. In this book Jim Webb states:"CAT II and  III approaches have lower landing  
minimums.....require special certification for operators,pilots, and aircraft." CAT II decision height is usually 100-150'. CAT III is the one that really scares us career pilots. Not only because we have to sit there and trust the Autopilot to fly the airplane to zero feet and runway centerline, but mainly because it's only a matter of time before some bean counter says" why do we need to pay these guys all of this money when the airplane can
land itself!" Some of the airplanes on FS2002 are equipped to fly these approaches. The 777 is probably the best example. Again, for simplicity sake, fly a coupled(that's Autopilot set to APPCH. and the Auto Throttles armed) approach. For a CATII your decision height(usually 100 or 150') is listed on the bottom of the approach plate.