The fundamental social unit throughout the Roman empire was the family.
From the early days of the Republic, the existence of the family centered entirely on the concept of paterfamilias – the male head of the household had the power of life and death over all members of the family (even the extended family). He could reject children if they were disfigured, if he questioned their paternity, if he had more than one daughter already or merely if he felt so inclined. He could also sell any of his children into slavery.
Gradually, over time, this extreme, almost all-powerful, control over one’s family (patra potestas) would diminish. However, this ironclad rule by the husband or father did not limit the power of the woman of the house. The home was the domain of the wife. While she was initially restricted from appearing in public, she ran the household and often saw to the education of the children until a tutor could be found.
By the end of the Republic, she was even permitted to sit with her husband at dinner, go to the baths, although not at the same time as the men, and attend the games. Later, women could be seen working as bakers, pharmacists and shopkeepers and, legally, women’s rights improved, for example, divorce proceedings could be initiated by either the husband or wife.
Source: Roman Daily Life
The Roman household was conceived of as an economic and juridical unit or estate
Only a Roman citizen held the status of pater familias and there could only be one holder of the office within a household. He was responsible for its well-being, reputation and legal and moral propriety. The entire familia was expected to adhere to the core principles and laws of the Twelve Tables, which the pater familias had a duty to exemplify, enjoin and if necessary enforce, so within the familia Republican law and tradition (mos maiorum) allowed him powers of life and death (vitae necisque potestas). He was also obliged to observe the constraints imposed by Roman custom and law on all potestas. His decisions should be obtained through counsel, consultation and consent within the familia — these were decisions by committee (consilium). These family consilia probably involved the most senior members of his own household — especially his wife — and if necessary his peers and seniors within his extended clan
Roman law and tradition (mos maiorum) established the power of the pater familias within the community of his own extended familia. He held legal privilege over the property of the familia, and varying levels of authority over his dependents: these included his wife and children, certain other relatives through blood or adoption, clients, freedmen and slaves. The same mos maiorum moderated his authority and determined his responsibilities to his own familia and to the broader community. He had a duty to father and raise healthy children as future citizens of Rome, to maintain the moral propriety and well-being of his household, to honour his clan and ancestral gods and to dutifully participate—and if possible, serve—in Rome’s political, religious and social life. In effect, the pater familias was expected to be a good citizen. In theory at least, he held powers of life and death over every member of his extended familia through ancient right but in practice, the extreme form of this right was seldom exercised.