A diamond's carat weight measures the diamond's apparent size
Simply put, the carat weight of diamonds measures how much a diamond weighs.
A metric "carat" is defined as 200 milligrams. Each carat is divided into 100 'points'. This allows for very accurate measurements down to one-hundredth of a decimal. A jeweler can describe the weight of a diamond under one carat only by its "points". For example, the jeweler may refer to a diamond weighing 0.25 carats as "twenty-five hands". The weight of diamonds over 1 carat is expressed in carats and decimal places. A 1.08-carat stone would be described as "point zero eight carats".
All other things being equal, the price of the diamond increases with the carat weight of the diamond because larger diamonds are rarer and more sought after. However, two diamonds of the same carat weight can have very different values (and prices) depending on three other factors of the diamond's 4Cs: color, clarity, and cut.
While you now know what carat means, it's also important to remember that a diamond's value is determined by all of the 4Cs, not just carat weight.