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 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.