In Britain, "fanny" actually refers to a woman's genitals and is considered somewhat of a bad word. "Bum" is the preferred word for "butt" in Britain. And a fanny pack is even referred to as a "bum bag" for this reason.
I've read that It's the lower private parts of a woman, her "down-below" organs. If you hear the Bee Gees Song "Fanny - Be Tender With My Love" you'll get the same answer.
