In this context I'd say it's a show or group of shows that have a 'culture' for lack of a better word, because there is either so much to the franchise, or such intense fan passion for it, that it's more than just a show you watch, it's a world you get invested in. For example Star Wars, Star Trek, Stargate, etc. There is way more to them than just watching the various episodes.
I like hearing people's personal definitions of different words. It's fascinating.
