A few years ago when I was still a newbie in photography, I was quite unsettled by the term "stopping down the lens", or anything to do with f-stop. To find out what photography authors write about this topic, I went to the bookstore today to look at some books. I found that some do not talk about f-stop, while others go into technical details which are not very helpful unless you have a scientific mind. In my camera club, the photography class does not explain about f-stop, yet we use this term all the time.
Here's how I would explain f-stop. Exposure is controlled by 3 things: aperture, shutter speed, and ISO. From the largest to the smallest aperture, the aperture number goes like this: 1, 1.4, 2, 2.8,4,5.6,8,11,16,22 . Each step up halves the amount of light entering through. Next, shutter speed. Shutter speed goes like this .... 1/4, 1/8, 1/15, 1/30, 1/60, 1/125, 1/250, 1/500.... . Again, each step up halves the amount of light entering through. Finally, the ISO sensitivity goes like this: 100, 200, 400, 800, 1600.... Each step up doubles the sensitivity of the receptors on the sensor. The exposure remains unchanged if you go one step up in aperture, and then one step down in shutter speed, while keeping ISO constant.
To stop down the lens is to reduce the exposure by one f-stop. This can be done by going up one step in aperture, or one step up in shutter speed. Now, in some cameras you may find some in-between numbers other than what I have listed up there. These represent partial stops. Another way to add or minus f-stop is to use the exposure compensation (i.e. EV) setting on the camera, which gives you increments of 1/3 stops or 1/2 stops.
Application: In photography it is more useful to think in terms of stopping up or stopping down the lens, rather than the absolute aperture or shutter speed settings. This is because ambient light is always changing and the camera automatically advises the user of the computed exposure. The photographer can either use eyeballing technique to fine-tune the exposure he wants, or he can check the camera's calculated exposure and then stop up or stop down as he requires (the camera's computed exposure is not always ideal!). Understanding what the f-stop does is key to understanding exposure, be it in natural light, studio light, or flash photography. Now you can go and amaze your photographer friends by throwing around the f word.... or rather, the f-stop word. Say something like "I think you need to go down one stop for this one," when all you really meant was "make the picture darker".