Coarseness is a quality of roughness or graininess. You can feel the sand's coarseness when you sit on a beach.
There are two kinds of coarseness, but they're both rough. When you talk about the coarseness of the soil in your garden or the corn meal you're making muffins with, you mean that the particles are large and granular. Another kind of coarseness involves speaking or acting in a gross or vulgar way — someone who swears a lot and makes dirty jokes is displaying coarseness. Both types of coarseness show a lack of refinement.