This is an offensive term used to describe people who have been declared brain dead by doctors. Sometimes after a serious accident, the only thing that a victim can do on his own is breathe. The person cannot think, speak or move. A person who slips into a coma is said to be a vegetable. Other than the breathing, there are no indications that the individual is alive.
Here is an example. *The young boy has been a vegetable for the past six months. An individual who leads a very boring, monotonous existence can also be said to lead the life of a vegetable.