A quadriplegic or quadraplegic is someone who is impaired in all four limbs (from quadra, Latin for four (4), and plegia, Greek for paralyzed); also known as tetraplegic (from tetra, Greek for four). Quadriplegia is caused by spinal cord injury in the neck, and is usually the result of trauma (for example, a car accident, fall, or shooting) or disease (for example, polio, spina bifida, or amyotrophic lateral sclerosis (ALS)/Lou Gehrig's disease).
The amount of impairment a quadriplegic or "quad" has is dependent on where in the spine the injury occurred and whether it damaged the spinal cord, as it possible to fracture or break the back without injuring the nerves. Usually, a quad's spinal cord is not actually severed, but was injured when the cord swelled as a result of the trauma and pressed against the walls of its column through the centre of the spine, sustaining permanent damage such as scarring.
Generally, the higher the location of the vertebrae injured, the greater the impairment, which can range to total paralysis, also known as complete quadriplegia. Christopher Reeve was a famous quadriplegic who suffered virtually total paralysis from the neck down as the result of falling off a horse; Stephen Hawking's quadriplegia is the result of a severe motor neuron disease, ALS. In the case of an incomplete injury, quadriplegics retain some feeling and/or movement below the neck, and some can even use their limbs and/or hands and feet. Paraplegics have suffered nerve damage lower down in the thoracic, lumbar, or sacral region of the spine, and only lose function in their lower limbs.
As you can imagine, injuries resulting in quadriplegia are devastating and require a long period of adjustment. Dependent on others for many or most of the activities of daily life, quads usually have a difficult time adjusting to their condition. Though most quads will experience some improvement in function with time and rehabilitation, there is currently no cure for these injuries. Nevertheless, quadriplegics can lead full lives and even engage in extreme sports: see the inspirational documentary Murderball, about full contact quad rugby, a Paralympic sport.
One of the many excellent sources of information on paraplegia and quadriplegia on the web is http://www.apparelyzed.com/.