Phantom limb syndrome is a neurological condition in which amputees perceive sensations from their missing limbs. These sensations include itching and sometimes pain, and are reported by approximately 70% of amputees.
This condition may be explained by the re-oranization of an area of the brain, the somatosensory cortex, in the months and years after the amputation.
The somatosensory cortex is a region of the brain which receives sensory information from the body. Every square millimeter of skin surface contains nerve endings which send sensory information to the somatosensory cortex. The surface of the body is "mapped" onto the somatosensory cortex.
The area of cortex devoted to each part of the body is proportional to the sensitivity of that body part. The face and hands, which are the most sensitive parts of the body, have large parts of the somatosensory cortex devoted to them, while the rest of the body is represented only by small parts.
Following an amputation, there is, therefore, an area of the somatosensory which would normally be devoted to the amputated limb, but which is no longer receiving sensory stimuli from that limb, making it temporarily redundant.
The plasticity of the adult human brain makes it able to adapt to most circumstances. It is well known, for example, that blind people have a heightened sense of hearing. This is because the visual cortex starts to process auditory instead of visual information.
Something similar is probably happening in the case of phantom limb syndrome. Other cells in the somatosensory cortex begin extending their branches and connecting to those cells in the area which would normally be devoted to the amputated limb. The area that was receiving sensory inputs from the amputated limb now begins to receive sensory information from a part of the body next to the amputated limb.
But, somehow, there still remains some imprint of the original function of those cells, so that, occassionally, their stimulation causes the experience of a sensation in the amputated limb.