forgive me if this is incorrect:
Ac courtesy circle is usually done in hunters. If you trot into the ring, and you wait for the judges bell/whistle, then you begin a medium large circle at the trot, halfway through you pick up your canter. When you complete the circle, you head for your first jump. *the c.c. Is usually done so that when you finish your circle you are going in the right direction of your first jump. It gives you a chance to get your canter before approaching your fence.
I also think that at some shows you are supposed to do a courtesy circle after your course too....but im not so sure with that one.