The walls of our cells are semi-permeable membranes and water moves across them by a process known as osmosis.
Osmosis makes water molecules move from the side of the membrane that has a lower concentration of salt to the side that has a higher concentration of salt. The process of osmosis ensures that the concentration of salts in all fluids, whether inside the cells or outside remains in the range required for their proper functioning.
Drinking salt water surrounds the cells of the body by a solution that has a higher concentration of salt than what it is inside the cells. Water is forced out of the cells due to osmosis, in spite of the fact that they are already dehydrates and this dehydrates them further till they can no longer function and die.