Ancient Greece was largely patriarchal, so men were always in power both at home and in politics, while women were relegated to lives spent mostly inside their homes raising children and weaving. These practices were less present in certain city-states such as Sparta.
Ancient Greece wasn't one unified country but a collection of city-states. Each had its own laws and customs, so the roles of men and women sometimes varied from one city-state to another. In the close-knit family structure of ancient Athens the father was the head of the house and the only one to spend a large amount of time away from the house. All men born in Athens possessed the right to vote in the assembly. They took up arms in the military when needed. Sparta, on the other hand, kept a full-time military comprised of all male citizens, none of whom had any say in government.
The women of Athens oversaw the affairs of the home. Women ate separately from men at dinner parties and were rarely educated. The primary role of a woman was to bear children and continue the family line. In Sparta, women enjoyed more acceptance, often appearing in public and receiving the same physical education as men. They did this because it was commonly believed that women in better physical condition would bear better warriors.