Clarity is a little subjective as it refers to the natural inclusions in a diamond. Diamonds form more than 50 miles inside of earth and are comprised entirely of carbon atoms. When there are impurities mixed in with the carbon, the diamond will have some color (this will be explained in a later section). When the diamonds are forming, any change in temperature or pressure can change the speed and formation of the diamond, in turn creating impurities. These impurities are called inclusions and come in many forms. From your basic carbon crystal (unformed diamond), to feathers, knots, and naturals. The list goes on and on.
Why is this an issue for some? The more noticeable an inclusion is inside a stone, the cheaper it will be. When buying a diamond, look for inclusions that are small and off to the side. Sometimes when an inclusion is in the center of a diamond you can see it with the naked eye. For that reason, I don't recommend buying anything below a grade of SI2. Personally, I think inclusions are interesting because they make the stone unique, like a fingerprint, where no two diamonds are alike.
The common diamond grades are below:
Flawless (FL) - No inclusions or blemishes are visible to a skilled grader using 10× magnification
Internally Flawless (IF) - No inclusions and only blemishes are visible to a skilled grader using 10× magnification
Very, Very Slightly Included (VVS1 and VVS2) - Inclusions are difficult for a skilled grader to see under 10× magnification
Very Slightly Included (VS1 and VS2) - Inclusions are minor and range from difficult to somewhat easy for a skilled grader to see under 10x magnification
Slightly Included (SI1 and SI2) - Inclusions are noticeable to a skilled grader under 10x magnification
Included (I1, I2, and I3)- Inclusions are obvious under 10× magnification and may affect transparency and brilliance