Definition: Patriarchal (adj.) describes a general structure in which men have power over women. Society (n.) is the entirety of relations of a community. A patriarchal society consists of a male-dominated power structure throughout organized society and in individual relationships.
A patriarchy, from the ancient Greek patriarches, was a society where power was held by and passed down through the elder males. When modern historians and sociologists describe a "patriarchal society," they mean that men hold the positions of power: head of the family unit, leaders of social groups, boss in the workplace and heads of government.
Feminist theorists have expanded the definition of patriarchal society to describe a systemic bias against women. As second-wave feminists examined society during the 1960s, they did observe households headed by women and female leaders. They were of course concerned with whether this was uncommon. More significant, however, was the way society perceived women in power as an exception to a collectively held view of women's "role" in society. Rather than saying that individual men oppressed women, most feminists saw that oppression of women came from the underlying bias of a patriarchal society.