The intermediate class at Worldwinds mostly refines the skills you learned in the beginner class.
When I took the intermediate class with Jason and Stephen in October 2006, we switched to smaller, more streamlined boards than were used in the beginner class. These were JP 180 "New School" boards. For comparison, I think the beginner boards are in the 200+ liter range. The JP 180s look more like real boards and less like floating tables. The JP 180 boards are still stable, but not as stable as the beginner boards.
We also used bigger sails, ranging from 4.5 to 5.5 square meters. The larger sails and smaller boards mean more speed and maneuverability. You should get a much better sense of how to control your direction on these boards.
In this class, you work on posture and positioning quite a bit. I suggest practicing as much as possible after taking this class so you have a chance to memorize the skills while they are still fresh in your head. The posture didn't really click for me until I got to the harness class. I probably would have had an easier time if I had practiced the next day after the intermediate class.
The first aspect of posture is standing so that you are more prepared to resist gusts of wind and so you don't have to use much strength to hold the sail up. If you're leaning forward a lot or your back feels tired, you probably need some help on your posture.
If you still hold the mast with your front hand, this class is where you start to migrate it to holding the boom. This will be a necessary skill for getting into a harness in later classes. This seems a little tricky because the mast won't be straight up and down like you probably held it in the beginner class. You'll need to adjust your idea of how to hold the sail.
Finally, you will try to move back on the board as you gain speed. This part is easier said than done. I still can't move very far back on the board. To be able to do this, you need enough speed and power in the sail so that the back won't sink as you move. If the back sinks, you'll quickly turn up-wind until you lose power.
Keep in mind that these are my personal thoughts and notes on the class. I'm a student, not an expert.