The Illuminated are Geniuses that have hit the bottom of the morality scale and are dangerously insane, even compared to a regular Genius. They are literally burning from the inside with the light of Inspiration, completely unfettered by petty concerns such as morality and human decency, living only to create and study, and may god help you if you get in their way or look useful to them. A Genius can become Illuminated if their Obligation becomes zero (Though this isn't the most common way, as by the time you get that far, someone usually kills you for the good of humanity. After all, a psychopathic Genius with massive amounts of power and no morality is not likely to make many friends), or after exceptionally failing an Unmada check while already being Unmada (by far the most common method). They literally lose all empathy and see humanity rather like how humans look at lab rats, as experimentation fodder.
Their minds have transcended humanity, becoming a conduit for something larger and more grand then humans are capable of understanding. Illuminated possess all the memories and abilities from before they became Illuminated. And most can simulate their old personalities as a mask of sorts. Unlike "normal" Unmada, you can never return to your prior state of mind once you become Illuminated.