4C's - Cut
Diamond cut is perhaps the most important of the four Cs, so it is important to understand how this quality affects the properties and values of a diamond. A good cut gives a diamond its brilliance, which is that brightness that seems to come from the very heart of a diamond. The angles and finish of any diamond are what determine its ability to handle light, which leads to brilliance.
As shown in the images below, when a diamond is well-cut, light enters through the table and travels to the pavilion where it reflects from one side to the other before reflecting back out of the diamond through the table and to the observer's eye. This light is the brilliance we mentioned, and it's this flashing, fiery effect that makes diamonds so mesmerizing.
In a poorly cut diamond, the light that enters through the table reaches the facets and then 'leaks' out from the sides or bottom of the diamond rather than reflecting back to the eye. Less light reflected back to the eye means less brilliance.
While diamonds come in many different shapes, including round brilliants, hearts, pears, and marquises, the cut has to do with proportion and the arrangement of facets.
For more information, view the below video.
This exert is from the GIA website.