The clarity of a diamond refers to how clear, or "clean" the diamond is. Most diamonds have "imperfections" in them. The clarity scale is a measure of the severity of those imperfections or "inclusions" as it is known in the trade.
For example, a deep break in a diamond which is not that visible when you look at the stone face-up, could sometimes have a greater impact on the clarity of a stone, than a small black crystal which you can see very clearly face-up.
The following is the Diamond clarity-scale:
FL-Flawless
These stones have no imperfections inside or on the outside of the stone under the magnification of a loupe of 10 power.
IF-Internally Flawless
These stones have no inclusions under a loupe with a 10 power magnification.
VVS1,VVS2-Very Very Slightly Imperfect
These stones have very small inclusions which are very difficult to see under a loupe with a 10 power magnification.
VS1,VS2-Very Slightly Imperfect
These stones have small inclusions which are slightly difficult to difficult to see under a loupe with a 10 power magnification.
SI1,SI2-Slightly Imperfect
These stones have inclusions which are fairly easy to see under a loupe with a 10 power magnification, or visible to the naked eye.
I1,I2,I3-Imperfect
These stones have inclusions which range from eye visible to very easily seen to the naked eye.