When you are planning to purchase a diamond it is important that you know as much as possible about how diamonds are classified. Today, the 4Cs of diamond quality is the universal method for assessing the quality of any diamond, anywhere in the world. Moreover, there's the "Fifth C" : Certificate

Diamond clarity refers to the absence of inclusions and blemishes

Natural diamonds are the result of carbon which was exposed to extreme pressure and heat deep in the Earth. Basically this natural process can result in two types of flaws; internal like air bubble, cracks and non-diamond minerals found in the diamond, or external flaws which includes scratches.

Flawless: No internal or external flaws. Extremely rare.
Internally Flawless: no internal flaws, but some surface flaws. Very rare.

Very Very Slightly included (two grades).
Minute inclusions very difficult to detect under 10 x magnification by a trained gemologist.

Very Slightly included (two grades).
Minute inclusions seen only with difficulty under 10 x magnification.

Slightly included (two grades).
Minute inclusions more easily detected under 10x magnification.

Tip: For grades F through SI a diamond's clarity grade has an impact on the diamond's value, not on the unmagnified diamond's appearance.

Included (three grades).
Inclusions visible under 10x magnification AS WELL AS to the naked eye. Not recommended.

Which Clarity Grade Should I Choose?
While Flawless diamonds are the rarest, a diamond does not have to be flawless to be stunning. Diamonds with VVS and VS grades are excellent choices for both value and appearance.

More affordable (and still a great choice) are those diamonds which gemologists call “eye-clean” – diamonds with no inclusions visible to the naked eye. These diamonds are SI1 and SI2 and unless the recipient carries a 10X loupe (a strong jewelry magnifying glass), she won’t see the inclusions.
As to I1-I3 Maybe when there’s a diamond grade that’s defined as “you can see the flaws just by looking at the diamond"