We'll probably do a lore update for them in the future, but here are the basics:
* Centuries ago, one man founded the fighting monastic disciplines. He was an old warrior who had knocked on death's door many times and had endured numerous periods of captivity and torture. He discovered a method of mentally focusing on his pain to invoke power from his soul. When he left the service of his lord, he devoted his time to developing these techniques and teaching them to other warriors (in this way, he can be seen as a sort of cross between
Ignatius of Loyola and
Suzuki Shōsan). He believed that mortification of the flesh not only made warriors more powerful, but that it strengthened the souls of its practitioners, making it more likely that their souls would remain intact (i.e., not fragment) when they died. He advocated fighting with bare fists and without armor to emphasize a fighting monk's personal suffering.
* Because the founder of these disciplines was old when he began teaching and died only a few decades later, there are now many different monastic orders. Some are more secluded, some are mendicant travelers, some are mercenaries. They all tend to believe, like their founder, that combat is the ideal path for pursuing their particular brand of mortification of the flesh. Some choose to pursue this in dedicated service, some become mercenaries or assassins, and others devote their lives to dangerous wandering and exploration. There are other groups that also practice mortification of the flesh, but they are not "fighting" monks.
* Monks believe in the fundamental philosophy of mortification of the flesh, but different orders and individuals have wildly different takes on it. Some monks (and entire orders) are very religious, but the founder was not religious and the discipline does not depend on religion. Most monks see the disciplines as a method of self-improvement that can co-exist with (or without) religious beliefs.