The Alliance is a Colonial term used to describe those under the subjugation of the Cylon Empire. (Saga of a Star World)
The Cylons, as to be expected, govern the Alliance. Members of the Alliance often relinquish freedoms and rights to the Cylons in return for their continued existence. They also work for the Cylons in some capacity.
For instance, the Ovions were members of the Alliance and operated a facade chancery on Carillon. The Ovions also mined tylium from the planetoid for the Cylons to use in their crafts.