Eye-clean means that the diamond has absolutely no inclusions that are visible to the naked eye. The best way to check this, is to look at the diamond in daylight through the top down. If we hold a diamond at any random, desired height, there may not be any inclusions, small or big, observed before we can speak of eye-clean. If so, the diamond is perfectly eye-clean. Obviously the observations can differ when an unknowing person or a professional expert, who already suspects an inclusion, takes a look at the diamond.