It's really all about geometry - nothing clever that you can't figure out from first principles on a sheet of paper:
Mark a point on a piece of paper, and draw lines radially away from it (saw 12 to start with - like on a clock. You may need to add more lines latter to get more acurate results). Thats your light source. Draw a line representing your object, so that a few rays of light land upon it. Each ray carries a fixed amount of energy. The amount of energy landing on your object is simply the number of rays which it it.
As you move the object further away, less rays of the rays it it. In fact in this case if you double the distance the number would approximatly half because we're working on a flat sheet of paper (it's onnly approximmate because we have only a few rays - in fact there would be billions of rays - aka photons, so in real life the result is almost exact). With a real ilght source the light wouldn't just be spreading up and down the page, but into and out of the page too, so a doubleing of distances half's the rays twice. A tripling of distance would divide the rays by three twice.
Another though experiment is to imagine a ballon, with a light source in the middle. All the energy from the light is illuminating the surface of the balloon. If you inflate the ballon the surface are increases, so the light is shared more thinly. In fact for each doubling or the radius, the surface area goes up by 4. If you marked a set of points on the balloon representing light rays, and an area on the ballon the number of points in the area represent the amount of light hitting it. Then inflate the balloon to twice its diameter, the area would now be four times the size, but has exactly the same rays hitting it, so the illumination (candles per square meter, or candles per square foot) has divided by four.
Ian