Rose Kennedy was the matriarch of the Kennedy clan — she was the female head of the family. This noun can also be used metaphorically. For instance, Alice Waters could be called the matriarch of Chez Panisse and the generation of chefs that her revolutionary restaurant inspired.
Although matriarch was created as a parallel term to patriarch, this eighteenth-century new creation was based on a false etymology. Although patri- might look related to the Latin pater "father," it actually comes from the Greek patria "family." Presumably, it was assumed that such a person would be a man. In any case, patriarch has come to mean the male head of a family or clan, while matriarch is used if the head of a family or clan is female.