This is the simplest of the 4Cs and the only 'C' that is not subjective.
A Carat or kt. is just a unit of measure for the weight of the diamond. It has nothing to do with Carat/Karat as in 9 carat/karat or 18 carat/karat gold which is a unit of Gold Purity.
One carat is equivalent to 200mg = 0.200 grams = 1/5th of one gram. ie 5 carats = 1 gram. Given it is measured with precise weight scales there is no need for human judgement. One carat is further broken up into 100 points. ie a 50 point diamond is 50/100 carats ie half a carat. Similarly a 0.10 carat diamond is the same as a 10 point diamond.
Value does not increase proportionately with carat size. For example a 1 carat diamond does not cost twice as much as a half carat diamond, nor 4 times as much as a 25 point diamond. It costs much more because as the size of a diamond increases so does its rarity.
Further, when viewed from the top don't expect a 2 carat diamond will look twice as big as a 1 carat diamond. The chart on the right is a guide to diameter increases in well-cut diamonds. As can be seen in the scale, a 2 carat round brilliant cut diamond will have a diameter approximately 8.2mm and a 1 carat diamond approximately 6.5mm. The reason is that the weight of a diamond is linearly proportional to its volume and not to its girdle diameter.
The diameter of a diamond will also depend on the cut to a certain extent. The sizes given in this table assume a well cut stone. Deep cut diamonds appear smaller than well cut (ie well proportioned) diamonds of the same weight and conversely shallow cut diamonds appear larger than ideal cut diamonds of the same weight. Read more on cut further down.
Another thing to consider when purchasing a diamond is that there is a premium price when they reach and exceed each 1/4 carat level. As an example a 0.99 carat diamond will be cheaper per carat than a 1.00 carat diamond. ie there is a larger jump in price from 0.99 carat to 1.00 carat than there is from 1.00 to 1.01 even though in both cases the diamond is only 0.01 carats bigger. So to save a little money, when looking for a 75 point diamond for example, you may as well buy a 73 or 74 point diamond if one is available at a better price. Be warned that some large on-line retailers offer 1 carat diamond rings and in the fine print mention the stone could be a minimum of 0.98 carats.