Recently I was struggling to understand how the Panasonic Lumix FZ200 could have a stable 2.8 lens across the entire zoom range.   To my mind the number was f/D where f = focal length and D = diameter.  Ergo it could not be constant.

There’s no change in the mechanical opening in a constant aperture lens. The iris doesn’t move, it doesn’t open wider, it remains the same. It’s all in the optical properties. 

As the magnifying front element/group moves relative to the iris, when you zoom it magnifies the aperture as seen from the front of the lens thus increasing the relative aperture and therefore maintaining the constant f-number. Constant aperture lenses are designed so that the entry pupil varies in direct 1:1 ratio with the focal length of the lens as you zoom.

The above is the words of a poster named VirtualRain over at MacRumors and it is perhaps the most simple way of explaining it I have seen.   They key is magnification and relative aperture.