Sassy means "bold or fresh." If you see your teacher in the grocery store with her attractive, well-dressed husband and you charge right over to say, "Who's the hunk?" that's being very sassy.
Sassy comes from saucy, as in: bold, spicy, and impertinent. It's fun to be sassy when talking with friends, but when you start saying things to teachers, bosses, and other people's parents that would embarrass a more timid or manners-minded person, you probably have crossed the line from sassy to inappropriate. The same goes for sassy dressers — you have to know when to leave the neon heels at home.