It is usually used in the context of fussy interfering old maid. A "biddy" is elongated in English by "old biddy", thereby describing a grandmotherly type person who invariably looks like and acts like she's sucking lemons. It comes from the rural areas I believe following the "fussing and clucking" of a mother hen around her chicks. Nice derailment of a thread there, and just with a photo of a fat man in a red suit.