The concept of mapping describes the relationship of the control layout to their function. Ideally, mapping should allow the user to understand how the function and in a way mirror the layout found in reality.
A good example of mapping that I found was the control for the heater in my room (which thankfully I did not need to use much this week because the weather was so nice). The control clearly shows that when turned to the left, the temperature becomes cooler, while turning to the right increases the temperature and makes the room hotter. The dial also clearly shows the user that the control can be twisted to provide a spectrum of temperatures. One minor problem with the control might be that there is limited visibility of system status in that there is no visual indication for weather the heater is actually running. It would be hard to visually see if the heater was broken.
A poor example of mapping is the control for the fan and light in my room. Rather than having a dial to change the speed of the fan, there are very defined settings. The mapping of the fan control does not really match with the function or increased fan speed. In other words, just showing me numbers does not really tell me much about the speed. Furthermore, the horizontal light switch is not only inconsistent with many other light switches, the left/right control for turning the light on and off does not map very well with our instilled concepts of turning things on and off.
A solution to improve mapping for the fan could be to include a twistable dial with small images that indicate increased wind speed, rather than numbers. The reason I believe that including a dial would be better mapping is because dials are more commonly associated with increasing strength as they are turned to the right, whereas switches are more commonly associated with on vs. off. Furthermore, I would move the light switch above the fan control because there the light switch is used more frequently, and I would make the light switch vertical to better represent on vs. off.