Symmetry is key when shopping for round brilliant (or ideal) cut diamonds. Much less so when it comes to fancy shapes or cuts such as an asscher cut or an emerald cut diamond. Round cut diamonds are cut with 57 facets (58 with culet), giving it more room for error if they don't align correctly, in which results to light performance being poor if not aligned correctly.
Examples that cause light performance to be poor because of symmetry include off-center culets and tables, an uneven or wavy girdle, and quite the common cause, misshapen facets. Lastly, if a crown and pavilion are not parallel, this will also have an effect on a diamond's sparkle.
A diamond with a higher clarity grade would be best supplemented with a quality symmetry grade. Symmetry should be less of a concern with lower quality grade diamonds.