Phantom limb pain is pain felt in a part of a limb that is no longer there after an amputation. Around 80% of people who have an amputation have some form of phantom pains. Researchers don't know exactly what causes this pain to happen, however we have a better understanding of it than we used to. At first phantom pain was thought to be psychological, however we know now that it has to do with the nervous system.
One explanation for why this happens is that the nerves in your spinal cord rewire themselves after they lose the signal from the missing limb and then pain signals are sent to the brain. One of the treatments is called mirror therapy which involves looking in the mirror of the limb that is still there (arm, leg, etc) for 20 minutes a day as you exercise. This tricks the brain into thinking that the other limb is still there.