It means you know something very well-- you know it from every possible direction. It is often used when talking about expertise. Think of it as your car. You know it from the rear headlight to the front headlight. You know it from the back to the front and from the front to the back. You know every part of your car. To know the alphabet backwards and forwards means you can say it "a, b, c, d, e..." and "z, y, x, w, v, u...". To be able to do that means you know the alphabet very well.