I've had a lot of my friends confused on this bit as well.

The main religion in Westeros is the Faith of the Seven.
So, when we see the Sept (church) or any religious regalia, it's a 7 pointed star. Each point represents one of the "forms" of God. There's the maiden, the warrior, the mother, the father, the smith, the crone, and the stranger (ie death). Sometimes you'll hear characters reference one of these. And a few episodes ago, when the High Septon (high priest of the seven) got caught in the whore house, one of the women had her hair covering her face. She was representing the stranger, whose face is never seen. Just a little background.

Ok so, with all the upheaval in Westeros since the War of the Five Kings, septs (churches) have been destroyed as well as septons (priests) along with the devout and faithful have been killed despite having nothing to do with the War and taking no sides in it. So the faithful began gathering the bones of those killed and brought them to King's Landing to lay them before the King and ask for protection. They got there and weren't attended to and became disillusioned with the corruption in the faith's clergy. It being well known that the High Septon for example was a frequent visitor in the brothels, for example. They became more fundamentalist bordering on a split with the Faith. Cersei, trying to maintain some semblance of power, is trying to take advantage of this group, and has decided to arm them and allow them to "police" the faith.