A picture frame mat is a board that is cut to have a window in it so that it borders your picture. You use them on things like pastels, watercolors, posters, and photographs. They are enhancers; basically, they add color to your artwork or keep the art from touching the glass. They come in all different colors and variations. Normally they are cut with a bevel so you see the core of the mat board. Some mats have colored core or black core, but the most common bevel is a white core. The other option is to have the mat cut with a reverse bevel. This is great when a bright white line might be distracting.
The difference between a single mat and a double mat is that there are two mat boards stacked on top of one another. They are usually different colors. Typically there is a top mat that you see a lot of its color and then there is a bottom mat where you see just a small amount of its color. The amount of this bottom mat is called the reveal. The reveal amount will default on most mats to being a 1/4". In my opinion mat reveals should be tweaked all the time. Play with the mat reveals make them 1/8" sometimes with a really bright mat color so you can really spice up your art. Or go the other way make it a 1/2" on a really big mat so you notice the bottom mat easier.