When a public official or his handlers demand, either directly or through third parties, that an average citizen apologize or beg forgiveness for having have hurt the official's feelings, and the everage citizen's defiance goes viral and forces the official in question into a humiliating climbdown in which the official winds up apologizing to the citizen instead.
After the mayor demanded an apology from a high school student for an allegedly disrespectul tweet, he got well and truly brownbacked by his angry constituents and had to say "I'm sorry."
Synonym for badass, beat, raw, dope. Someone or something that inspires awe. Being brownnasty is the peak of one's life. Few accomplish it, but the ones that do elicit fervent admiration and become members of the brownnasty crew.
Patel: Hey bro, I heard you're the backup qb at Alabama. You must be getting all the chicks, right?
Chandelle: Hell yeah man. More threesomes then I can even count. It's safe to say I'm brownnasty.