Anything covered with or resembling moss is mossy. A mossy rock can be pretty. Mossy teeth are never pretty.
Moss tends to grow in a green carpet, especially in wooded or shady areas, so when you're walking through a forest you'll probably come upon mossy areas. Informally, you can also use this adjective to mean "old fashioned" or "dated." Your grandparents' conservative ideas about dating, for example, might be a little mossy. The word stems from an Old English root, meos, that's a close relation to mos, or "bog."