[spoiler]As reprisals for the capture of Tyrion, Tywin unleashed the Mountain on the Riverlands. Gregor did what Gregor does: burned peasants, looted women, raped castles. Ned Stark, then hand of the king, ordered one of the knights at court (ser Beric Dondarrion) to take a hundred men with him and capture Gregor Clegane. That was back in season 1.
The brotherhood (their full name is “the brotherhood without banners”) are the remains of those hundred. They’re now outlaws for following their original orders, but engage in guerilla warfare behind the Lannister lines. Since the Mountain is such a personable fellow, the common folk of his lands give their support to the brotherhood against him - hence the constant torturefest in Harrenhal (at least, up until Jaqen killed the torturer at Arya’s behest)[/spoiler]