The Maximals are a noble faction of Transformers that existed during the Beast Era of Transformers G1 continuity (at least the G1 cartoons and Marvel comics). Founded some time after the end of the Great Cybertronian War, they arose to become the leading society of Cybertron, bringing about an era of peace the likes of which had not been experienced since the Golden Age. Details behind the origins of the Maximals are sketchy, but it is known that they are descended from the Autobots and, as such, are peaceful by nature. However, the Great War made it clear that strong military power would be required to ensure that peace was maintained, leading to the formation of the Maximal Imperium as Cybertron's governing body.
The Predacons - Cybertron's other major faction during the era of the Pax Cybertronia - harboured deep grudges against the Maximals and many of them believed themselves to be treated as second-class citizens. Given that the Predacons are descended from the Decepticons - who had attempted to conquer much of the known universe only to be defeated in the War - this doesn't come as surprising. The Maximals may rule by democracy, but they remain wary of their Predacon citizens, and rightfully so.