Why is it that if my back itching and I scratch - the itch always moves to another part of back?

When you scratch an itch, you are essentially activating the nerve cells that transmit the itch sensation to your brain. This can give temporary relief from the itch, but can overstimulate the same cells in the immediate area (which is the area you just scratched). Scratching can thus temporarily dampen nerve cell activation in one area while exciting activation in nearby areas of skin—which gives the sensation of the itch "moving" when in fact its just the excitation moving around your back as you scratch different itch centers.