You can buy a colorless (white) diamond, that is of flawless clarity, but if it is cut poorly, it will be dull and lifeless. The cut grade represents how the facets have been cut, the angles created and the overall depth of the diamond. Diamonds sparkle because they are designed to return light to it's source.
When a diamond is well cut, lights enters through to top (the table), bounces around the facets in the bottom half (the pavilion) and return back out of the top creating the sparkle and scintillation that makes them beautiful. However, if it is poorly cut, facets are misaligned, or the pavilion is too deep, light will leak out of the bottom and sides and the brilliance we come to expect will be muted and unimpressive.
When you search for a loose diamond, start with an excellent or ideal cut and then adjust the color, clarity and carat weight to fit your budget. You and your partner will end up with a product that you will keep staring at for years to come!