A diamond's cut is often confused with its shape (for a display of diamond shapes click here).

The term 'cut' actually refers to the quality of the craftsmanship that yielded the diamond.  A well crafted or cut diamond will possess proportions that will allow the diamond to maximize its brilliancy and ability to shine.

The above picture illustrates the way light interacts with diamonds that have varying width and depth proportions.  Diamonds that are well proportioned lose less light inside of the stone and instead project that light outwards.  This effect causes the diamonds to look more brilliant and "full of life".