Why is injury to this part usually fatal?

It depends on the part you mean. If you get a hole in the thoracic cavity, then you can't breathe. If you get sliced in the neck, you'll never stop bleeding. If you get stabbed in the thigh, then you'll bleed too much blood out. If you get an injury to the brain you could lose brain cells that might never come back. This is bad because you won't have the knowledge that you need.