For any latitude, one can precisely calculate the mean extraterrestrial solar radiation (the radiation striking the top of the atmosphere) for any month of the year. HOMER does that. So when you enter the monthly mean radiation at the surface, HOMER immediately divides that by the mean extraterrestrial radiation to calculate the clearness index. Similarly, if you chose instead to enter the clearness index, HOMER would immediately multiply that by the extraterrestrial radiation to calculate the mean radiation at the surface.
So the clearness index and the mean radiation are just different ways of saying the same thing.