A carat is a unit of measurement for the weight of a diamond with one carat being equal to 200 milligrams, or 0.2 grams, also known as 100 points. Since larger diamonds are harder to find than smaller ones, the price of diamonds with respect to their carat weight goes up exponentially.
Two diamonds of the same weight could have different sizes. Why? If a diamond is cut too shallow (or flat) it will have a larger diameter, but shallow depth and appear larger. Likewise, if a diamond is cut too deep (or pointed) it will have a smaller diameter and deep depth and appear smaller. This is why cut is so important.