The Illuminati are a secret society, existing beyond even the Emperor's knowledge, but manipulating and interpreting the Imperial Will to bring about their objectives.
Every member is a part of the society by virtue of being "illuminated" through the experience of daemonic possession, and finally salvation. Possessed by a daemon, they have done what seems impossible, exorcising the daemon from their body through their own sheer will.
In most cases, a daemonhost does not survive possession - the victim is eventually driven insane, or the mind is driven out of the host body so that the daemon takes complete control of it. A daemon can exist indefinitely within a host, with the possessed host often continuing their mortal life. Sometimes a strong-willed host can put up some resistance and preserve their self within a tenuous corner of the possessed brain. The host mind survives as a mere helpless witness as the daemon uses the mortal body to wreak its terrible acts. In a few instances, however, an individual has managed to cast the daemon from their body.
The Illuminati have been 'illuminated' to the terror of Chaos. Sharing a mind with a daemon, they have gained the most intimate understanding of Chaos. Having mastered the Chaos within themselves, they are immune to its temptations and corruption, and they now fight it in the broader universe. As they share a common enemy, the Illuminati are frequently involved on some level with the Eldar, in particular the Harlequins. The Illuminati are some of the very few allowed access to the Eldar's Black Library of Chaos. They know of the Fall of the Eldar, and seek to prevent the same from happening to Man.
The Illuminatis' experiences have brought them to a level of harsh realism that has no equal. The Illuminati are devoted solely to mankind's preservation. Ultimately, this goal involves plotting to bring about the rebirth of the Emperor of Mankind. They realize the Emperor's mind is failing, His will fragmenting into warring parts, and that there will come a time where the Emperor has deteriorated to the point where His will finally breaks. Without the Emperor, mankind will fall to Chaos. The Illuminati plan to rejuvenate the Emperor by sacrificing His descendants, the Sensei, at the moment the Emperor's will finally fails. The Emperor will be reborn, as the Sensei-Emperor, to again lead humanity directly. Their plans are a carefully kept secret; should the Emperor learn their plan, He may see no reason to continue to endure, and allow Himself to die prematurely. Should the Sensei learn, they may be unwilling to meet their intended fate.
The Illuminati influence events to pave the way for the Emperor's rebirth, and gather together the Sensei, protecting them from the persecution of the Inquisition.
The Ordo Malleus of the Inquisition know of the Illuminati, considering them dangerous heretics. They fear the Illuminati's plans are influenced by Chaos. The Ordo Malleus are devoted to wiping out the Illuminati and Sensei whenever they come across them, while in this secret war, the Illuminati engage in a campaign of confusion and disinformation against the Ordo Malleus.
Many Illuminati are also Inquisitors, which gives the brotherhood much more power and influence.
Furthermore, within the Illuminati there is an even more extreme faction known as the Ordo Hydra that seeks to save mankind by linking the mind of every individual through a warp entity known as the Hydra, thereby psychically unifying mankind into one being under the control of the Ordo Hydra themselves.
The Illuminati were introduced in the Realm of Chaos books alongside the Sensei and Star Child background material.