The role of women in Ancient Greece was typically rather circumscribed. Greek women typically had very little role to play in their society. However, this was not completely true in every city-state.
In most Greek city-states, women had very little role in society, particularly outside the home. Women were typically expected to stay at home all of the time. Of course, this would not have been possible for women who were not fairly well-off. Poor women might have had to work and would certainly have had to do things like going shopping. But the ideal was that women would remain in the home at all times except for things like religious festivals.
The main role of women was to bear children. Their secondary role was to care for the children and the home. This could be done either by the woman herself or, among wealthier women, by supervising servants. Women were typically trained for this role from early childhood since they would be married when they were 14 or 15 years old.
There were, however, exceptions. The one of which we know the most is Sparta. In Sparta, women were expected to be much more a part of public life. They were expected to maintain physical fitness. They could own property. They had to do much more in public life because the men were often away fighting or training.
Thus, most Ancient Greek women played very little role in public society, but this is not true of all city-states.