'The Church', as it was ironically called, was an organization set up by the Empire of the Hood to control and monitor all of the Earth's religions. From a basic point of view, it was there to keep the religions of the world from fighting each other, but what it was actually there to do was militarise the religions of the world and turn them into an army for the use of the Hood. Even long after the death of Hood and the dissolution of the Empire, the Church lived on. Towards the end of its reign, the Church had become corrupt, twisted by the idiot Colonel Failure and turned into an army of war, war against one thing in particular. The Doctor.
Despite the massive military strengths of the Church, its armies were decimated by the Doctor's companions and the Church was officially disbanded after that, finally allowing the religions of Earth to continue as normal.