Carat weight is the weight of the diamond measured in carats. One carat is divided into 100 "points," so that a diamond of 75 points weighs 0.75 carats. Carat weight is the most obvious factor in determining the value of a diamond. But two diamonds of equal carat weights can have very different prices, depending on their quality. Diamonds of high quality can be found in all size ranges. Since diamonds are measured by carat weight, and not size, two diamonds of the same weight could have different sizes. Why? If a diamond is cut too shallow it will have a larger diameter but a smaller depth. Likewise, if a diamond is cut too deep it will have a smaller diameter and thus appear smaller when viewed from the top.
Cut is very important. A properly cut diamond will both yield a good face up size and sparkle well. For example, let's say you're interested in a 1.00ct round diamond. A poorly cut diamond that is really deep would only have a diameter of approximately 6.1mm. So not only are you short changed on the face up size, but you get a diamond that was not cut to its full potential and thus does not sparkle like it should.