"A household of sensible jacketS" (plural) is a household (family) in which everyone is the kind of person who wears a sensible jacket. A sensible jacket is exactly as Hilary explained. (I see you are watching 'About Time'.)

household of sensible jacket - is nonsense, it doesn't mean anything. 'A sensible jacket" is something your aunt might tell you to wear if you were going out in cold weather. "Sensible shoes" is another such phrase - my mother was always lamenting that young girls wouldn't wear sensible shoes - instead of the four inch high heels they teeter about in. In other words, put practicality before fashion and vanity and wear clothes appropriate for the weather.