A household was a group of individuals, consisting of a family and any servants, all of whom occupied the same home.
Spock's medical file indicated he had grown up in a traditional Vulcan household. (DIS: "Point of Light")
(TOS: "Requiem for Methuselah")
In the rest chamber after Captain James T. Kirk slept and woke up, Vanna was questioned by Droxine, who asked why she had come into the rest chamber, to which Vanna replied, "To welcome our honored guests as I was taught to do when I served in your father's household." (TOS: "The Cloud Minders")
(DS9: "Cardassians")
(DS9: "In the Cards")