The girdle of a diamond separates the top of the diamond (crown), from the bottom of the diamond (pavilion).  The girdle of a diamond can be polished, faceted, or bruted (rough).  The girdle is an integral part of a diamonds cut for two reasons:  
1.  Should the girdle be too thin then there is an increased chance of the diamond being chipped.
2.  Should the girdle be too thick then too much additional weight is stored in the girdle making the stone look smaller from the top then a stone it's weight should appear.  A thick girdle can also negatively affect the sparkle (brilliance) of a diamond.