A patriarch is a male leader / head of a family or tribe. A matriarch is the female equivalent.
A patriarchal society is one where those in control are male.
The term patriarchy is used to describe the state of our society where significant gender bias still exists – where certain roles are considered the domain of males, with others being typically associated with females.
It’s important to note that it therefore places artificial gender roles on both males and females. However, it is described as a patriarchy because the bias puts significantly more men in positions of power than women.
For example, despite the fact that about 50% of the population of the earth are female, as of September 2016 only 7 percent of the top 1000 American companies were led by women. And less than a quarter (23%) of national parliamentarians worldwide are women. The UN Women website has lots more facts and figures if you are interested.
Conversely, there are certain professions that have a much higher proportion of females – such as primary school teachers and nurses. This is less of an issue in terms of the privileges it grants in society, as these roles tend be less prestigious and less well paid, but, nevertheless, men wishing to enter these fields can encounter some stigma.