The water in the radiator is the same as in the engine, the water pump pumps it around the engine where it absorbs the heat then out through the radiator for cooling, then back in the engine again, and so it goes on.
The dark murkey colour suggests it is well overdue for a change of antifreeze, or that someone has put some rad seal type stuff in there because of problems.
Have you just got the car ?, make sure the expansion tank is only filled to minimum.
tabetha