Circles help the horse gain balance and strengthen thier backs. A nice collected frame won't happen (or won't be consistent) with a weak back. If you notice in the video the horse's butt is dragging behind him and hollow through out his back.. He improves some what when she starts circling to the left because you can tell he feels more balanced to the left. On the first left circle infront of the jumps you can see him trying to stretch down and then again and when he does this he steps further underneath himself a little more because he is lengthening his stride and that would be a good starting point. Let your horse build up back and neck muscle first and then ask for more and more with smaller circles. The smaller the circle the more he is forced to bring the inside leg underneath him to stay balanced.
MIEventer is giving you a good example of what alot of riders are doing these days. I use to hear "leg to hand and seat to hand" and think "ok.... what does this mean?" If you look at MIEventer there are several frames where she is posting ahead of her horse. She isn't effectively using her seat and pushing him to her hand.
Lunge lessons always help to improve your seat and your legs which will also help you in your quest for collection.