It sounds like you are looking for a legal definition. Is there a tax, homesteading or # of animals issue that you're trying to figure out? If that's the case, it's going to differ from place to place and I'm not sure anyone is going to be able to answer that for you unless they live in the same community.
Im not really looking for the definition for any reason in particular, just that i heard it on Countryfile and wondered what it meant, ive got chickens and ducks but dont have it as a business just sell the eggs to friends and use them ourselves.
It is a term that is used outside of the USA. I know here in my state the same thing is refered too as hobby farm. One can take right offs based on it also. Basicly what it means is that you grow your own food and might sell either veggis or animals but it is not your sole income.