Given that every human is necessarily the product of a male and female human, every step in our ancestry forks. Every person has a mother and a father. Each of their mother and father also has a mother and father, etc. Every generation is a fork.
“Matrilineal” means tracing ancestry through the mother – it literally means “mother line.” Taking the “mother’s fork” in each generation.
A “matrilineal society” is one that customarily traces heritage through maternal lines, rather than paternal (“patrilineal”).
Why I Looked It Up
In Cutting for Stone, a character realizes who someone’s father is, and comments on why they had never pondered the question before:
Was I the only one to not know this? […] True, in a matrilineal society, one accepted these things and didn’t ask about a father when none was present.