Basically, a religous group that empowers its members by sharing Common Magic, rather than giving them the ability to call for Divine Aid from a diety (or any other Otherworld-based benefit). Aside from the worship's personal "spin" on the kind of Common Magic that is shared, this is really no different at all from just taking Common Magic. Note that membership in a Common Magic Religion does not automatically give Common Magic abilities -- it is, essentially, color, from a rules point of view.