Docs description is a good one, I will just add that in my experience they usually get noisy before they go, anything from a screch to a rumble, but they make noise, and usually leak as well, as long as it and the impeller is truning though it should still be doing its job and cooling the car, I would be surprised if the water pump as far as cooling (even though I understand the logic behind the thought, doesn't cool well, water pump helps cool the engine, water pump may be bad).
If the pump is bad you can almost always tell by taking the belt off and as the doc said chaking for lateral movement and terning it by hand to see if it turns smooth and quiet.