Clarity is a measure of the number and extent of the flaws in the
diamond. Generally speaking, the fewer the flaws, the more
valuable the diamond. Completely flawless diamonds are extremely
rare -- only a few hundred "FL" diamonds are produced
per year worldwide.
There are several grading systems used to describe clarity.
By far, the most popular and the diamond certificate most smart
diamond shoppers should demand, is the Gemological Institute of
America's (G.I.A.) scale, which ranks diamonds as Flawless (FL),
Internally Flawless (IF), very very slightly included (VVS), very
slightly included (VS), slightly imperfect (SI), and imperfect (I):

Although seemingly subjective, the G.I.A. scale has specific criteria
that are used to differentiate between the different grades (what's
the difference between "very very" slight and "very"
slight anyway!):
FL: Completely flawless
IF: Internally flawless; only external
flaws are present, which can be removed by further polishing the
stone
VVS1 - VVS2: Only an expert can detect
flaws with a 10X microscope. By definition, if an expert
can see a flaw from the top of the diamond, it is a VVS2.
Otherwise, if an expert can only detect flaws when viewing the
bottom of the stone, then it is a VVS1
VS1 - VS2: You can see flaws with a 10X
microscope, but it takes a long time (more than about 10 seconds)
SI1 - SI2: You can see flaws with a 10X
microscope
I1 - I3: You can see flaws with the naked
eye. Consider avoiding I2-I3 diamonds.
There are many different types of flaws. The best way to
become acquainted with them is to look at lots of diamonds.
The more common ones are as follows:
Pinpoint: A very small white dot on the
surface of the stone. By far, the most common flaw
Carbons: A very small black dot on the
surface of the stone. Less common than pinpoints
Feathers: Small cracks within the stone,
similar in look to broken glass. Small internal feathers
are harmless (other than lowering the clarity rating of the diamond),
but large feathers can become a problem because the crack can
grow as the diamond ages
Clouds: Hazy areas within the diamond,
actually made up of many small crystals that are impossible to
see individually
Crystal Growth: A small crystalline growth
within the diamond. Looks like a small diamond within the
big diamond
Unfortunately, clarity is very difficult to judge accurately by
an inexperienced consumer, so your best bet is to gain an education
first by looking at lots of diamonds before making a purchase.
Any good jeweler will spend the time you need to get comfortable
judging the clarity of your stone -- ask different jewelers to point
out the flaws in several stones until you can detect pinpoints
and other flaws by yourself.
One pitfall to avoid when shopping for clarity is the "clarity-enhanced"
diamond. This is an artificial process used to "fix"
the flaws on an otherwise good stone. Although a clarity-enhanced
diamond can look nearly flawless (in some cases, it is impossible
to detect the enhancement), it is intrinsically worth as much as
a flawed stone. Furthermore, the durability is nowhere that
of pure diamond. Be sure to confirm with your jeweler that
the stone you are considering is not clarity-enhanced, and be sure
to double-check this fact on the G.I.A. certificate. If you
do not receive a G.I.A. certificate with your stone, ask the jeweler
to state that the diamond is not clarity-enhanced on the appraisal.
Many people make clarity the least "important" of the
4 Cs when purchasing their diamonds. The rationale is obvious
-- when your partner shows the ring to all her friends, the likelihood
that one of them will pull out a 10X microscope to examine the flaws
on her diamond are very slim. Given that, why spend a lot
of money on a VVS1 diamond when an SI2 will look exactly the same
to the naked eye?