Subtlety is the quality of being understated, delicate, or nuanced. You can really appreciate the subtlety of your gothic friend's art if you can distinguish among many different shades of black.
The Latin root of subtle and subtlety originally meant "finely woven" and was used to describe fabric. The subtlety of an argument is in the fine weave of the words and thoughts that it is made up of. When translating, you often lose the subtleties of the original language, the interlacing of word, idea and connotation. When you're trying to persuade your parents of something, subtlety might get you further than outright demands.