This was a war fought between the Galactic Council, a prominent leadership of certain sections of the Galaxy, and the Reachites of New Reach. The war stemmed from Jorgey's Master Plan, in which Jorgey created a new Reach from the wreckages collected by Requiem's portal, and used the Composer and his own DNA to create a species to inhabit the planet, which he dubbed Reachites. The Galactic Council saw the Reachites as abominations, but could do nothing about them because New Reach was located in League territory.
Eventually though, the Reachites began to expand. They went across the boundaries of League territory and into Galactic Council space, in which they began attacking civilian populations of planets, believing them to be blastphemous as their planet was not like Reach. The Galactic Council responded aggresively, annihilating sections of the Reachite fleet and eventually driving them back to New Reach. The League did nothing to stop the Council's advances up until this point when, as the Galactic Council encircled New Reach, they attacked. With hordes of Reaper, Covenant, Human and Republic ships they drove the Galactic Council forces back and utterly devastated their fleet. Jorgey stepped in at this point to resolve the conflict, and negotiations began. The entire Reachite fleet was confiscated and the Reachites were exiled to New Reach.
After this the Galactic Council fell into decline, only managing to maintain its grip over a handful of worlds in the resulting negotiations. The Council itself had already been crippled after the Galactic Credit Crunch and very few races remained in the Council following the Reachite war.