Cut refers firstly to the overall shape of the diamond. Secondarily and most importantly, cut refers to the proportion of the cut. For certified round brilliant cut diamonds the cut is graded in terms of its cut and finish; polish and symmetry. If a diamond is not well cut then it will not have the same beauty and brilliance as a well cut stone.
Regarding the overall shape of the cut, there are several different shaped cuts of diamond that are relatively widely available in a range of sizes, for example round brilliant, princess, marquise, pear, oval, heart, radiant and emerald cut. Also there are dozens more unusual and less available cuts like kite shape, shield cut, and trilliant. Some design houses have even created their own branded cuts of diamond.