To draw some modern day parallels (from reality and fiction), The Order is a combination of:
Alcoholics Anonymous, in that it was created to help save the lives of people dealing with a life-threatening addiction.
The Jesuits, in that it is secretive, at least semi-religious, and tolerates no dissension.
The CIA, in that its purpose is to interfere in the affairs of foreign governments for mutual benefit, whether they like it or not.
The Jedi Council, in that members are extensively trained to become super-soldiers who wield vast physical and magical powers.
The origins of The Order are shrouded in mystery, but most credible evidence points to a pact made between a prodigiously talented assassin and a nobleman he had been hired to kill. The assassin’s training and experience had allowed him to exploit his Gift, which had pushed him into the top tier of his profession. To his chagrin, however, he channeled too much power and, in the midst of a job, he was attacked by demonic forces attracted by his flagrant magic use. In a twist of fate, he was rescued by the very nobleman he had been commissioned to assassinate. It turned out that the nobleman was targeted for assassination due to his strange and increasingly aggressive behaviour – side effects of his untrained magic use. The two formed a friendship and, eventually, the basis for a continent-spanning organization.
The physical location of The Order’s headquarters is also a mystery, though it is thought to be on a lower level of an Ordin Region.
The Order exists to protect the world from magic. This entails both protecting mundanes from wielders of magic and protecting wielders of magic from themselves.