Quick vocab lesson first. The diagram below shows the parts of a faceted gemstone. I don't know that you'll be able to work this info into regular conversation, but knowledge is power.
What may be of more use to you, however, is the terminology around the way stones are shaped and how they're cut. Stones are cut and ground into specific shapes to enhance the way light reflects and refracts within them and to bring the focus to a specific section of the raw material. Cutting and finishing gemstones is known as lapidary or lapidary arts. The technology used varies from computerized faceting machines to sandpaper. There are large shop versions and table top or hand held wet saws and grinders.
Cabochons, or cabs, are flat backed stones. They're often the first type of stone jewelry students learn to set. Lately, a specific type of cabochon, druzy, has become very popular. They're essentially a collection of crystals on the surface of another stone. Here's more information on how they're formed. Mickey Lynn's website also has great information.