The term 'carat' refers to the weight of a diamond, and not the size. One carat of diamond weighs 200 milligrams or 1/5th of a gram. One carat of diamond can be divided as 100 points of diamond. As such, this can then be divided down, so that 50 points of diamond refers to half a carat of diamond and 25 points refers to a quarter of a carat of diamond, and so on.
Many people consider the carat to be the main factor that determines the value of a diamond, as in many instances the bigger the diamond, the more you'd expect to pay. However, this is not the sole factor in determining a diamond's wealth, and should not be the only factor taken into account, as the other C's can have a big impact.
Two diamonds of the same carat may differ dramatically in value, if their colour and clarity are extremely different. So it is important to remember to check the other factors alongside the carat, and not just assume that the higher the carat weight, the higher the value of the diamond, as this is not always the case.