The next step, once you've learned how to level your pelvis, is to learn to move that level pelvis as you walk and run. This happens by allowing your pelvis to rotate in the direction your rear leg swings. This rotation is crucial to injury prevention and efficiency. By allowing your whole lower body to rotate around the vertical axis, you can gain from 1 to 4 inches with each stride. Any amount that your pelvis rotates along with that leg as it swings behind you will add inches to your stride and ease the amount of work done at the hip joint. A longer rearward stride (without the heel striking that comes from overstriding) can reduce the amount of impact to your knees, hips and lower back. In addition, rotating your pelvis around the vertical axis allows you to tap into a very powerful set of core muscles deep within the abdomen - the iliopsoas. This big muscle elongates at the back of your stride. Then, as your foot leaves the ground, it naturally recoils from its stretched position which returns your leg to the support phase of your stride without engaging your quadriceps.
... I go one step farther and tell runners to imagine that their legs begin at this juncture point (T12/L1). If your entire lower body rotates from this point, while your upper body remains "fixed," your running will be much more efficient and easier on your body. On the other hand, if your pelvis doesn't move when you walk or run, it means that all of the swinging motion of your legs originates at your hip joints. Over time this can create overuse injuries in the hip area such as hip bursitis, hamstring pulls, IT Band inflammation and hyper-extension of the hip flexors, especially when you try to run or walk faster with a bigger leg swing.
With some strides this feels natural to me, with others (such as running on inclines) it does not. I had always avoided twisting at the lumbar spine, but recently learned to do it correctly (using hip muscles) for 3-turns in ice skating. I want to find out in what other activities I should use these newly discovered muscles.