Clothes moths, of which there are two common species (the Common/Webbing Clothes Moth and the Case-bearing Clothes Moth), belong to the family Tineidae. They are small, and hold their wings roof-like over their body when at rest. Both of these species have adapted to feeding (in the caterpillar stage) on stored fabrics, especially wool, but many other natural fibers are at risk as well, and stored produce is also accepted by them as a food source. They are considered a serious pest because of the amount of damage they can cause due to their larval feeding.
Additional Information: Clothes Moths (University of Kentucky)