Providing food and water (also called nutrition and hydration) through artifical means is a way of getting calories and nutrients into the body when a person can't eat naturally. It may involve the use of a tube inserted into the stomach through the nose, or inserted surgically through the skin and stomach wall. The tube can deliver nutrition, water and medications. Fluid and medications can also be delivered through an intravenous (IV) line. Artificially provided nutrition and hydration serve different but related purposes, and are often discussed as a single topic.
People who are diagnosed as severely cognitively impaired (what you or I would call brain damaged) and who are not actively dying should - indeed must - be given food and water, through a feeding tube if necessary. And by the way, no one should ever be described as a "vegetable." It is used to insult and dehumanize the person to whom it is applied. A more appropriate description would be that the patient is in a non-responsive, rather than vegetative, state. After all, a human being is not a tomato, and every human being deserves proper care for as long as he or she lives.
The moral use of nutrition and hydration - or the moral withdrawal of nutrition and hydration - is dependant upon the particular circumstances. Allowing death to occur naturally is very different than intending to cause death to occur unnaturally. Food and water, warmth and shelter are natural and humane means of providing comfort - not extraordinary means, and certainly not burdensome treatment.
If a person is dying of a terminal disease, and is unable to process food and water, (no matter how it is delivered, by mouth, intravenously, or tube feeding) then there is no moral or medical obligation to provide such nutrition or hydration. However, if a patient is not dying, then food and water must be provided. To argue otherwise leads to the discriminatory assumption that patients in a coma, or a non-responsive state, or who are suffering from Alzheimer's or dementia, are qualitatively different from other patients.
That assumption leads to the value judgment that some lives are not worth living, that the life of a patient in a non-responsive or impaired state is not meaningful. In so doing, the inherent, intrinsic dignity of all human beings, regardless of ability, is unjustly ignored.