Matron is the senior female in any given House.
She is the only female allowed to give birth to children. She also sets policy, appoints thos who fill any posts and so on.
Usually she is helped in this by her daughters.
The most powerful (and hopefully the oldest) daughter is expected to succeed her eventually through rights of power. When a Matron is no longer capable of keeping her daughters from killing her, she no longer deserves to be a Matron. This is the accepted way of things and a daughter who succeeds her mother without killing her herself is noty really considered a "proper" matron.