When you lose a limb in an accident or operation, you expect it to be completely gone. You expect to have no feeling from it anymore, as it doesn't exist anymore. Yes? No.
Although the limb in question itself has been removed, the section of the brain which controls it is still intact. Some people can still feel the limb as if it's actually there. Sometimes they can describe the limb; and it normally tends to be very different to the other; shorter or longer, fatter or thinner. Very often the area in which the limb existed beforehand appears to be painful, due to the severance of nearby nerves; but in other cases, the person can actually sense the limb and can feel it moving as he or she tries to move it. The feeling a young child must get when trying to grab something with an arm that isn't there must be unbearable, as they wouldn't be able to understand why the object isn't moving since they did move their arm after all... didn't they?
Why Does this Happen?
Specific areas of the brain control specific areas of the body. This means that by putting a low electrical charge through the section controlling the shoulder would trigger a feeling in the shoulder. However, these areas of the brain controlling parts of the body are not placed in any particular logical order. For example, the section that senses the side of the face is directly next to the section that senses the side of the hand, and the section that senses the foot is directly next to the section that senses the genitals. This means that touching the side of the face of a person who has lost an arm could also trigger a feeling in the hand that isn't there. An image of the body is mapped out in the sensory region of the brain. This body image is called a homunculus. There is also a less well-defined homunculus for position (proprioception), movement, and so on.
If a limb is removed, the homunculus is still intact, and so the brain tries to 'fill in' the missing gaps, hence the phantom limb experience. This can manifest itself as a feeling of heat, pressure or intense pain. Sometimes the phantom limb phenomenon can manifest itself as a feeling that the missing limb is gripping something (for example, a missing hand may relentlessly crush itself into a fist). This is because the brain uses a combination of visual stimulus and a built-in positioning sensor mechanism (proprioception) to work out where a normal limb is. When a limb is missing, these mechanisms fail, and so again the brain 'fills in' the missing information, often doing a very bad job of it.
Can this Be Overcome?
Relief from pain in phantom limbs is difficult to achieve by normal means, such as painkillers. However, there is a new and devilishly simple way of easing the proprioception problem; position your limbs so both your hand and your missing hand would rest on the table in front of you. Place a mirror vertically between the hand and missing hand, so the reflection of your existing hand looks like it is where your missing hand is. This tricks the brain into seeing the visual feedback for the missing hand, allowing you to mentally straighten it and release it from its grip, so to speak.