Your lesson will help you to carve on steeper slopes, icier runs, and at higher speeds. Carving in these conditions requires a greater edge angle of your stance ski. If the stance ski is insufficiently angled to the snow, the ski will simply let go and start skidding sideways, or your turns will grow larger while your speed increases. Carving and edging on modern skis become much stronger and more reliable if the stance leg remains longer and the hips move into the center of the turn arc. However, just edging the stance ski harder by trying to press on the big-toe edge or driving the knee into the turn doesn't accomplish the performance goals you have set.
How, then, do we achieve a greater edge angle of the stance ski without twisting, digging, or pushing on the stance leg? By using the Phantom Move and shortening the free leg. The combination of flexing the free leg and pulling the knee up and into the chest will drop the hips into the turn, bringing the body farther inside the arc of the turn. Once the hips are inside the turn, the stance ski will automatically roll to a higher edge angle.
Learning to flex the inside leg much more than the outside leg is much easier when we widen our stance. Simply being on a slope makes one leg bend more than the other. We'll take advantage of this to learn to flex the inside leg and to trust how the stance ski feels and arcs at the higher edge angles.