A lot of Native American tribes were matrilineal instead of the typical patrilineal societies you see from Europe. This meant that you were descended from your mother’s clan, not your father’s. It was also meant the women were involved in the decision-making process for the greater good of the tribe. Some of the more well-known matrilineal socieites are the Lenape, Hopi and Iroquois. The Chickasaw were also a matrilineal society.  
Source:  http://www.powwows.com/matrilineal-societies-women-with-power-and-respect/


 “Matrilineal” means property is passed down through the maternal line on the death of the mother, not that of the father.

Source: https://en.wikipedia.org/wiki/List_of_matrilineal_or_matrilocal_societies


Société matrilinéaire – Une société dans laquelle les liens de famille sont établis à partir des liens de famille de la mère, ou lignées matrilinéaires, et non à partir des lignes paternelles.