An ash coating is found on many goat cheeses from the Loire Valley in France and also on cheeses made elsewhere in the style of these cheeses.
One reason for the ash is purely decorative. It serves as a mark of distinction on this type of cheese. However, there are also good technical reasons. First, the ash is used to temper the acidity of the cheese. (Obtaining the proper acidity, which can be achieved through a variety of means, is a major consideration in cheesemaking, and not just for goat cheeses.) Second, the ash forms a surface that encourages the growth of desirable molds that affect the flavor of the cheese.
Ash can also be found inside a few cheeses. The French cow's milk cheese, Morbier, has a layer of ash in the center. The cheese was originally made by combining two milkings: the evening milking and a second milking the following morning. Right after the evening milking, a layer of ash was spread over the milk to prevent a skin from forming and also to discourage unwanted pests, like flies. With today's production and storage methods, the ash isn't really needed, but vegetable ash is still included because people think that is what Morbier should look like. The American goat cheese, Humboldt Fog, also has a thin layer of ash in the center in imitation of Morbier.
I'm a sucker for ashed goat cheeses too - especially the gooey, ripe ones like how Bonne Bouche from Vermont Butter and Cream or a classic selles-sur-cher can get.
From what I understand, ash was used to control mold formation on the outside of the cheese. I'm sure other people can pipe in with more details.
I'm usually to busy around these beauties to contemplate anything other than how to sneak another bite!