For something that the vast majority of Christmas carolers know nothing about, we sure get do get demanding about figgy pudding. Sheesh. Have you ever thought about how weird it is to demand some kind of gross-sounding pudding at least nine times in one song ... in which you're supposedly wishing someone a merry Christmas? What exactly is this fabled figgy pudding?
In short, figgy pudding is pretty much exactly what it sounds like -- a pudding/cake type thing with figs in it. The reason that it's in such high demand, however, has to do with some of its (inedible) ingredients.
Coins, rings and other trinkets were often hidden in the bowls of Christmas pudding and each supposedly predicted their recipient's fortune for the coming year. For example, if you found a coin, you would become wealthy. If you found a ring, you'd get married ... and so on. Think of it like an Old English fortune cookie.