Matrilineality and Patrilineality
Matrilineality is a system in which one belongs to one’s mother’s lineage. A matriline is a line of descent from a female ancestor to a descendant (of either sex) in which the individuals in all intervening generations are female. In a matrilineal descent system (uterine descent), an individual is considered to belong to the same descent group as his or her mother. Logically, it is easier to identify who the mother of a child is than the father.
In some cultures, membership of a group is inherited matrilineally. Example : Minangkabau culture of West Sumatra (Indonesia). Their culture is matrilineal, with property and land passing down from mother to daughter, while religious and political affairs are the province of men (although some women also play important roles in these areas). Other examples are : the Nairs, Bunts and Kurichiyas of Kerala, India, the Khasi and Garo of Meghalaya, India, the Naxi of China, and the Gitksan of British Columbia and the Iroquois Confederacy (Haudenosaunee).
Patrilineality is a system in which one belongs to one’s father’s lineage. It generally involves the inheritance of property, names or titles through the male line as well. A patriline is a line of descent from a male ancestor to a descendant (of either sex) in which the individuals in all intervening generations are male. In a patrilineal descent system (= agnatic descent), an individual is considered to belong to the same descent group as his or her father. Example: In Roman times, all citizens were divided by gens and familia, determined on a purely patrilineal basis, in the same way as the modern inheritance of surnames. (The gens was the larger unit, and was divided into several familia: a person called “Gaius Iulius Caesar” belonged to the Julian gens and the Caesar family.)
Source :
http://en.wikipedia.org/wiki/Matrilineal
http://en.wikipedia.org/wiki/Patrilineality