Matrilineality is a big word that means that people trace their family history through their mothers. Just like when you draw a family tree in school, you can see your grandparents, your great-grandparents, and so on.
In matrilineal societies, the family tree starts with the mother, not the father. For example, if your mom was from a matrilineal society, your family tree would show your mom's mother, her mother, and her mother's mother, and so on.
This is different from patrilineal societies, where people trace their family history through their fathers. If your dad was from a patrilineal society, your family tree would show your dad's father, his father, and his father's father, and so on.
Matrilineality is important because it gives women and their families a special status and authority in their society. Women are respected and valued as the head of the family, and they are often the ones who pass down traditions to their children and grandchildren.