The only girl in her family, Touma's the tomboy of class 5-1 who happens to share the Minami surname—though she's got no actual relation to the famous Minami sisters. Still, Chiaki decided to adopt her as a little brother anyway, mostly as a joke about the name thing. She's got three older brothers back home who have absolutely no idea what she's up to at school, and their influence pretty much shaped how she acts now: rough around the edges, dressed down, the whole deal.
She pulls off the boy act so convincingly that Fujioka genuinely believed she was male. Chiaki's explained the "younger brother" thing by pointing out that Touma's name contains the kanji for winter, and since winter comes after autumn, logically Touma has to be the younger one. It's the kind of logic that makes sense if you don't think about it too hard.
Content compiled by AnimeList.moe from publicly available sources.