In the late 30th Millennium, when a world was liberated -- or subjugated -- by the military forces of the Great Crusade, or willingly joined the ever-expanding domains of the Imperium of Man, it was said to have achieved "Imperial Compliance" or simply "Compliance."
Having conquered the entirety of sacred Terra during what were to be named the Unification Wars, the Emperor of Mankind looked to the stars, intent to reconquer those worlds humanity had lost during the baleful centuries of the Age of Strife. After forging the compact with Mars, the Emperor now commanded immense armies of human soldiery as well as the beginning of what would eventually grow into the Legiones Astartes, the Space Marine Legions.
As the Emperor undertook His mission to reunite the scattered human colony worlds of the galaxy and free humanity from the xenos and Warp-creatures that had nearly destroyed it, He conquered world after world, exterminating the mutants and aliens that had threatened Mankind's rightful place amongst the stars. Where human society had survived, it was made part of the Imperium, or rather it "Achieved Compliance with the Imperial Truth" as the parlance of those great days would have it.
Sometimes these integrations were achieved through diplomacy and the promise of a better future and the restoration of humanity's great stellar empire. Often it required a show of force to subjugate planetary rulers and dynasties that had been used to governing their worlds for Terran centuries and even millennia. Even more often, Imperial Compliance had to be obtained by force of arms. In these great wars, tyrants were cast down and witches burned, planets purged of the foul taint of mutants, xenos and Warp-beasts such that eventually these campaigns of planetary conquest became known as Imperial Compliance campaigns or, more simply, rendering a world "Compliant."
These Compliance campaigns were carried out by every military branch of the Imperium: from the countless regiments of the Imperial Army and the coldly-logical ranks of the Mechanicum Taghmatas to the towering representatives of the Titan Legions of the Collegia Titanica, but greatest amongst these were the Space Marines. Countless worlds were brought into the fold of the Imperium by these gene-enhanced warriors, at whose heads stood the eighteen Primarchs, the Emperor's own sons from whom the Space Marine Legions had been raised.
Yet even these multitudes were not enough to police and control the entirety of the Emperor's domain, and while some of the Legions indeed erected mighty keeps and fortresses to keep watch over the newly Compliant populations -- most notoriously the Imperial Fists, the Iron Warriors and the Ultramarines -- many were the Primarchs who refused to squander their warriors to such "administrative" tasks.
But peace had to be maintained and every world's culture reshaped according to the mold of the atheistic Imperial Truth. The Great Crusade's ever-growing need for supplies, starships and manpower also needed to be satiated. As a result, the Emperor devised a grand plan, the installment of the Great Tithe, which every world of the Imperium would have to submit itself to. In accord with the Tithe Grade established by the newly founded Office of the Administratum, every world would offer up its most precious resource for the Emperor: whether this be supplies, precious minerals, rare crystals or chemical compounds, weapons and ammunition, tanks and voidships or even just its manpower.
Entire planetary populations were moved and sent to colonise planets far from their homeworlds, while the most troublesome and dangerous peoples were pressed into Imperial Army regiments and sent to the frontlines of the Great Crusade. For many more warlike cultures, such as the many Knight Worlds that populated the galaxy, this was in itself an immense recompense: the chance to gain glory and renown amongst the stars.
Later, after the Great Crusade ended in the darkness and horror of the Horus Heresy, the Warmaster Horus, the Archtraitor, would initiate a new Compliance regime as he sought to create his own shadow empire. This action became known as Dark Compliance. In this way, the Warmaster did not annihilate what had come before him, but would pervert what he had helped establish in new and terrifying ways.
- The Horus Heresy - Book One: Betrayal (Forge World Series) by Alan Bligh, pg. 22
- The Horus Heresy - Book Four: Conquest (Forge World Series) by Alan Bligh, pg. 17