People often have tension in the lumbar area of their backs which has the effect of pulling the back forward, sometimes accentuating the natural curve there. When I work with this sort of back it feels as though the person is dividing themselves in two - top half and bottom half.
The same problem often occurs with horses, where the dip in their backs will be dropping, thus cutting off good coordination between the two ends of the animal. Trying to function with this distortion is really inefficient and will lead to fatigue, likely pain and even possible damage.
The aim of Alexander training and dressage training is to get an integrated muscular system, with freedom in the neck and support from the legs/hind quarters. In order to achieve this, one of the things we need to focus on is the back 'staying back'.
Lying down in semi-supine is a good way to practice this:)