a house: the building a family lives in, and by extension the people who belong to it, from a single household to a whole family line
At its core this word names a house, the place where a family lives. But the Bible rarely stops at the bricks. The same word slides easily from the building to the people inside it, so "his house" can mean Peter's home or Peter's whole family, and the reader has to feel which one the writer means.
From there the word stretches in two directions. Upward, the most important house in Israel is God's house, the temple, and Jesus calls it "my Father's house." Outward, a household is not just one generation but a line that runs through time, so "the house of David" means David's royal descendants and "the house of Israel" means the whole nation seen as one family.
These are not separate words but one word doing connected work. A house holds a family; a family becomes a lineage; the gathered people of God are themselves called his house. The thread running through every use is belonging: a house is defined by who lives in it and who comes from it.
This is why translators have to choose. Greek lets one word carry the building, the family, and the dynasty at once; English usually cannot, and the choice between "house," "household," and "family" is an interpretation, not a given.