This function basically allows you to identify caches that you and another person (a) both have found, (b) both have not found, or (c) one of you has found.
Imagine you want to go on a tour with a friend and are looking for a good route. When you know the region (say, your state or county), do the map compare for that region, checking the option fields you want to search. The map will then show you all matching caches (these can be several thousands if the region is large). Try to enter another person in the upper right and select a region of your choice below, plus check the first two or three checkboxes below that. Does it work now? You will note that caches are shown in different colours depending who found them so your can select what route to take.