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”).