The diamond shape refers to the overall style / shape of the diamond. Due to its popularity and the fact that it minimises wastage a Round Brilliant Cut (RBC) still commands higher prices than some other shapes although increasingly this is changing.
With the advent of computer design tools and indeed computerised cutting, we are seeing some more unusual diamond shapes, from the relatively simple heart shape, to much more elaborate designs.

Diamond shape and diamond cuts are closely linked. While the shape gives an overall look to a diamond, the quality of the cut and relationship of the facets are the prime factors that define a diamonds brilliance.
Some diamond shapes are better at optimising refraction than others. This is one of the reasons why a round brilliant cut (RBC) is so sought after. However, a unique or unusual diamond shape will often still have excellent refractive properties and suits people who like to have something a little different.