The Braus family is a family of hunters living in Dauper, a settlements in the territories of what were the Wall Rose. It is the family where Sasha Braus hails from.
Story: Sasha's father argued with his daughter, telling her not to eat the meat that was saved for the winter. After he failed, he explained his daughter the reason why it was important to keep the food: after the fall of Wall Maria, many refugees had come to Wall Rose's lands. They started to hunt animals making their number decline, hunting the preys that belonged to hunters' villages, like Dauper.
Trivia: Braus (Brauss) comes from the German saying "in Sauß und Brauss leben", meaning "to live off the fat of the land", a phrase she herself quotes.
Source: Braus family (Anime), available under CC BY-SA 3.0.