It sets the virtual range that AH will bother rendering graphics for. For instance, on short range view, that moutian range way off in the distance will disappear, as well as the individual trees, and other ground objects on the terrain until you get closer to them. The net effect is that your pc is not rendering those graphics, so it is able to produce frames at a faster rate. Seeing others planes are not affected by the range setting except at extreme dot distances.
While I upgrade components on a regular basis, my pc is nearly never top of the line, so in a dogfight when I really want great frame rates for gunnery, I will switch over to short range vis. I normally cruise with full vis.
Medium vis is somewhere in between.
Ground vis is very important when GVing. Not only does Vis range affect ground objects, but also ground vehicles. It is possible for distant GVs to be invisible if you have Vis at a lower setting. In ground vis, everything that should be in your view is rendered at its full appropriate graphic detail. Obviously that makes it the hardest on your frame rates.
Also, I believe only full vis is directly tied to your graphic detail and range settings. Medium and short vis will arbitrarly not render things beyond a set distance range, and ground vis will override your settings.