It's short for Carat (Ct) Total (T) Weight (W)
Carat is the measuring unit of diamond weight. The definition of a carat has changed over time, but since 1913 the international standard has been 200 milligrams, or 1/5 of a gram (1/142 of an ounce). One carat is divided into 100 parts, called “points.” So, a 25-point diamond weighs a quarter carat and a 50-point diamond weighs a half carat. A diamond may be referred to as a 3/4-carat or 75-point stone. Jewelers usually express diamond weights in carats and decimals. A 1.09-carat stone, for example, is said to weigh “one oh nine carats” while a 0.99-carat diamond weighs “ninety-nine points.”
“Carat total weight” (Ct. T.W.) describes the combined total weight of all the stones in a piece of jewelry having more than one diamond.