Cut - Precision and Brillance
Cut is pivotal in giving a diamond it's brilliance and sparkle and refers to the overall porportions of a diamond. A precise and ideal cut diamond will reflect the maximum amount of light that enters it, making it appearly lively and sparkle.

It's good to be on the receiving side of a diamond. Having that little sparkling rock on your hand and there's no other care in the world.
Carat is a measure of weight of the diamond and not actually the obvious "size" of the diamond, as is commonly thought. Diamonds are measured by weight with 'points' and 'carats' as the unit of meaure (1 carat = 100-points = 0.2 grams or 0.007 ounce). The more points or carats, the larger and more rare the diamond.
From colorless to yellow, a diamonds color refers to the grade assigned to indicate the color spectrum the stone falls within.