Amyotrophic lateral sclerosis, or ALS, or more colloquially Lou Gherig's Disease is a progressive neurological disorder which eventually robs the body of it's ability to control its muscles. During this period of time, the mental faculties of the patient remain intact. It can strike at any time during adulthood and, once diagnosed, it is progressive and eventually fatal. During this period of time, the patient eventually becomes fully paralyzed to the point of no longer being able to talk in many cases, but in all cases to the point of quadriplegia.
One of the most famous sufferers of the disorder, apart from it's original namesake, is physicist Stephen Hawking, who has lived with the disease since he was a student at Oxford and has managed to survive for over forty years.
In DNR, House turns out to be right when he meets an ALS patient and attempts to find a different diagnosis.