Carved relief depicting the Paterfamilias with his wife and two sons.
The term paterfamilias refers to the head of a Roman family, meaning "father of the family". The family encompassed all of the family members in the male line, and all their possessions, including slaves and animals.
The paterfamilias had legal authority over the whole family and could even sell his son three times to slavery (though this power was rarely used). The paterfamilias could exercise patria potestas -- the power over his family. He was also the religious head who had duties associated with the household gods.
In The House of Batiatus, Titus Batiatus is the paterfamilias and it is upon him to maintain the well-being of the household.