In ancient Greece, women did not have the same rights as men. This is because society at the time was a patriarchal society, which saw men as superior to women.
When looking at the cultural expectations of an ancient Greek woman or wife, you might first of all want to point out that women were expected to submit to the will of men, particularly the will of their fathers and, once married, the will of their husbands. As men were considered to be the head of their family, women were expected to obey and not to question this position of authority.
Another cultural expectation of an ancient Greek woman or wife would have been to look after the household. Richer families had slaves, in which case the wife would have been in charge of the slaves. If a family didn't have any slaves, then the wife would be expected to deal with all the household chores herself.
However, you might want to argue that the biggest cultural expectation of a Greek woman was to get married and to provide her husband with children. Marriage was usually arranged by a woman's father, and the woman would have been expected to accept her father's choice, irrespective of her own.