Utility means useful. You've heard of a utility knife, or a utility shed? These are useful items because of their versitility. Utilitarian means useful as well. Utilitarian art is art that has a useful purpose, such as a box, mug, pot, vase, etc. These art items can be highly decorated, but ultimately they are useful. As we look back through history, we see that even cave artists made their utilitarian items beautiful by carving or painting on them.
Non-Utilitarian art means art that is meant to be looked at aestetically, art that is pretty on the walls or nice to look at as a sculpture. Non-Utilitarian art is decorative. It can move you emotionally or spur you into action through depicting social themes, but it has no physical use other than as something to look at.
Sixth grade students have been working on clay manipulation, learning how to change clay into objects by using pinch, coil and slab for construction methods. They are presently working on a Utilitarian object that is decorated with relief and incised artwork. Some are making mugs, bowls or plates. But all the objects have both a useful purpose and a beautiful design to them.