As the other folks have said an eq or equitation class judges how well you ride the horse. To go into a little bit more depth, the judge will be looking at your position: is your weight sunk down into your heels, is there a straight line from your shoulder to hip to heel etc. They aren't supposed to take your horse's performance into account, which can be good if you have a horse who isn't a brilliant mover. That being said, it's always easier to look good on a horse that's responsive and comfortable to ride. And you should also note that wrong leads and breaking will still get you docked major points. More often than not the judge will have you work without stirrups (usually trotting sometimes cantering), so be sure to practice riding without them at home if you aren't already.
I hope that helps a little. I'm sure I left some stuff out, but in general that's they way it goes.
If someone could remind me, do they do pattern work in equitation classes? I haven't shown in one since my 4-H days XP I've gotten too used to western horsemanship where a pattern is pretty much a given.