Fairy cake can refer to several kinds of cakes.
Some people use the term to refer to a cake with nuts and/or dried fruits in it, usually unfrosted, sometimes in 2 layers with a cream or jam filling. Then, of course, there is the cake either in the shape of a fairy or with a fairy, or fairies, decorating it.
However, when I think of fairy cakes now, I think of what I grew up calling cupcakes.
I discovered this divergent nomenclature about two years ago, when a friend of mine mentioned that a British co-worker had a yen for fairy cakes. Neither of us knew what they were, so we went hunting for the answer. We found it on the web in a variety of recipe forums. This of course sparked a flurry of fairy cake baking, and the results were shared with all the children I knew at the time.
Likely named for fairies because of their diminutive size and often colorful decorations, I've seen recipes that are based on spongecake or, much less frequently, butter cake, often with fruits, nuts, or other interesting bits mixed into the batter. Although decorating is apparently not imperative, the most common decoration I found in my search is a layer of tinted frosting or icing which is then lightly dipped in multi-colored tiny round sprinkles. Excessive quantities of frosting is apparently not considered appropriate, although fancy frosting is another matter entirely.