Those who advocate the God Incarnate believe that the Emperor is a god, and like the other gods He exists within the Warp. They believe that just as a man such as the Emperor could become a god, it stands to reason that a god could become a man. This is the central idea of the God-Incarnate, the physical vessel for a God in the material world. These physical vessels, referred to by Thorians as Divine Avatars, would be special individuals who would become a host for the Emperor's consciousness in the Warp.
The myths and legends surrounding the God-Incarnate tell of the coming of the Divine Avatar(s) amid a time of great upheaval and war. Moreover, the Divine Avatar will possess unique traits such as phenomenal psychic power, an "altered" form, and the ability to talk to animals. Some within the Inquisition believe that the End Times represent this final period where the God Incarnate will finally be made manifest.
The principles of the God Incarnate are outlawed by the Inquisition, for they fear that if the Emperor were to be reborn, the Astronomican might fail, the Divine Avatar might be corrupted by Chaos, and civil war between believers and unbelievers would erupt. Moreover, the Emperor could be killed again, potentially taking the Emperor's essence with it. Thus some within the Inquisition have made it their duty to seek out possible Divine Avatars and either kill them or study them.
Meanwhile, the Magi are also seeking out Divine Avatars, except in their case they wish to prevent the second coming of the Emperor or perhaps use these mortal vessels to instead bring a Chaos God into the material universe.