Insane difficulties are the hardest difficulty in the general 4 difficulty mapset. These maps are generally exemplifications of the mapper's skill, and are the difficulties where creativity can be easily shown. Some other difficulty names have been applied with similar meaning as "insane", like Lunatic ("crazy", as it appears as the hardest difficulty in Touhou series), Another (IIDX beatmania series), Extreme (Jubeat Series), etc.
An issue with Insane maps is that they can be Overmapped to increase the map's difficulty.
Note that this is only a general suggestion. The difficulty setting varies depending on the song itself and mapper's own style.