Clarity, as the name implies, refers to how clear the material is that the stone is made of, and what surface imperfections it may have. These have a direct effect on how light passes into a diamond and bounces around within it before finally exiting.
The internal flaws are called inclusions and they appear for several reasons, usually either foreign material within the diamond or even another diamond crystal inside it or an imperfection such as a tiny crack in the structure of the material itself.
Surface imperfections are popularly called blemishes and they can be either major or minor and will affect the value of the stone accordingly.
Clarity is determined by the number, size, color, location, orientation and visibility of the inclusions and blemishes as seen under a 10X magnification. As mentioned earlier, flawless stones are very rare, so it is likely that you will be considering stones that are less than perfect. That's perfectly fine, particularly as many of these imperfections are scarcely visible to the naked eye and often only when you are scrutinizing the diamond very closely.
Here is a chart showing how diamonds are graded for clarity.
Flawless No flaws internally or externally.
Internally Flawless No flaws internally. This category of diamonds is also very rare and valued highly.
VVS1, VVS2 Very, Very Slightly Included: Very difficult to see inclusions under 10x magnification. These diamonds are high quality.
VS1, VS2 Very Slightly Included: Inclusions are not visible to the naked eye. This category is less expensive than the VVS1 or VVS2 grades.
SI1, SI2 Slightly Included: Inclusions are visible under 10x magnification. This level of clarity is considered by many to be the best value buy because the inclusions are not visible to the naked eye. The prices for these diamonds are notably lower compared to those in clearer categories.
SI3 Slightly Included-EGL: This is a category of clarity that is promoted by and is not certified by the Gemological Institute of America or other gemological institutions. Diamonds in this category are likely to be graded by GIA as either SI2 or I1. EGL distinguishes these diamonds as having no black inclusions or cracks that are visible to the naked eye, but they may posess some very minor white inclusions which are visible to the naked eye.
I1 Included: an I1 clarity diamond will have a visible flaw which can be seen with the unaided eye. If your budget is limited and you can only afford diamonds in the SI3 or I1 clarity, be sure to examine them under 10X magnification yourself before making the purchase. It will help you decide which one to buy. Any reputable jeweler would be happy to show you how to use a magnifier.
I2, I3 Included: The inclusions in this category of diamonds will be visible to the naked eye. They will have many black spots from the black inclusions and may appear cloudy from the white inclusions and cracks.