Permissiveness is a kind of freedom. Your family's permissiveness might mean that you don't have chores, a specific bedtime, or a curfew — unlike your friends with strict parents.
Sometimes people use this word to imply that there's too much lenience; they might talk about the permissiveness of schools nowadays, allowing students to use their phones in class or call teachers by their first names. When norms and rules change in a society, this often results in more permissiveness. It was once considered unseemly for women to wear pants, and changing fashions were seen as permissiveness. The Latin root, permittere, means "to let go or let loose."