In as quick (my wife is telling me that dinner is ready
) and as simple terms as possible, a Category C (or Mode C/Charlie) transponder is basically a transponder that also broadcasts the altitude of the aircraft together with its position. If the other aircraft was not 'squawking' Mode C, they would not know its altitude and that would explain the captain's comment of "he could be at 500 feet, he could be at 15,500".
My colleagues will no doubt be able to elaborate further without their dinner 'being in the dog'!!!
