A matriarchal family refers to the family structure in which the female is the head of the family; this is mainly in the context of the breadwinner. The mother then passes down their power or propriety down to the daughters of the family to reproduce the structure of a female-dominated family.
This challenges the stereotype of the traditional patriarchal or nuclear family; feminists would strongly argue that females have just as much capability of acting as breadwinners as men do, and the matriarchal structure strongly demonstrates the fluidity of contemporary society.