Carat is just a diamond industry special word for weight of a diamond stone. One carat is equal to 200 milligrams, or in other words, a 5-carat stone weighs 1 gram. The word carat originates from the Greek word kerátion, which means carob beans, which were known in the ancient world for uniformity of their size and weight and were used as a measure of weight for different objects, including gemstones.
In the Far East instead of carob beans jewelers used rice grains to determine the weight of gemstones. Because of this fact, you may occasionally hear some jewelers referring to a 1-carat diamond a four grainer, which means in the past 1 carat was equal to four grains of rice.
The weight of smaller diamonds is often expressed as points, not carats. One carat is equal to 100 points. Thus, for example, a 10-point diamond has the weight of 0.1 carats.
Diamond prices typically increase at a higher rate from one weight / price bracket to the next. For example, price per carat for diamonds in the size bracket 1.00-1.49 carats could be $8,000, while price per carat in the bracket 1.49-1.99 carats can jump to $11,000.
To maximize the size of the purchased diamond without having to pay a higher price per carat, it is therefore better to buy diamonds with the size towards the higher end of a chosen price bracket:
For example, buy a diamond the size of 1.48, rather than 1.51 because the size of these stones would most likely be priced according to different price brackets. Thus, 1.48 carat diamond would be priced at 1.48 x $8,000 = $11,840 while 1.51 carat diamond would be priced at $11,000 per carat and thus would have the value of 1.51 x $11,000 = $16,600, that is $5,000 more for just 0.02 additional carats.