In a broad sense an imperial cult is any religion in which a head of state is worshipped as God. Examples of real (historical) civilizations with an Imperial Cult include Ancient Egypt and the Japanese Empire. On /tg/, it almost always refers specifically to the state religion of Warhammer 40,000's Imperium of Man, and basically Catholic Juche in Space.
It got its start from the Lectitio Divinatus, a spess bible written by Lorgar, Primarch of the Word Bearers, on the worlds conquered by his Legion during the Great Crusade and further perpetuated by believers amongst the crusade fleets. The Emperor, an advocate of atheism, did not approve, and chewed Lorgar out for it, which pushed his son into the worship of Chaos instead, which in turn ended up setting the Horus Heresy into motion. Afterwards, the Imperium worshiped the atheist even more than ever before. Just as planned.
After the Heresy, the Emperor was entombed in the Golden Throne and was not exactly in a condition to stop people from portraying him as a god, and it was soon discovered that humanity could be united by using this religion to control them far more effectively than the old Imperial Truth ever could. It's anyone's guess as to what he thinks about the whole mess now.
The Imperial Creed
Though the substance of the Imperial Creed can vary from world to world as the Imperium is extremely vast, the Creed itself is deceptively simple. This makes life easier for missionaries who are attempting to bring new planets into the fold as the original superstitions of each planet might be fundamentally incompatible with a convoluted religion with too many doctrines.
Regardless of any other deviations in belief, the basic tenets are as follows:
- Worship the God-Emperor of Mankind as the One-True-God, your Lord and Savior.
- Humanity is perfect and are the dominant form of life in the galaxy, everything else needs to be crushed or subjugated.
So at its simplest, a world can believe whatever it likes, so long as the Emperor is God or at the very least the head God, so on some worlds he might be a god of thunder and lightning, on others he might be the judge of the dead, on others he might just be an almighty paymaster, whilst on others he might be seen as a god of destruction who must be appeased with death... essentially each planet can have its own view of the Emperor. This makes the Imperial Cult an extremely tolerant religion when it comes to expressions of faith, which is ironically at odds with most observers' opinions on what the Imperial Creed is actually about.
The Imperial Cult and the Imperium
Where people get confused is with the distinction between the Imperial Cult and the Ecclesiarchy, which are distinct from one another; just as the worship of the pagan Roman Emperor was to the specific rites carried out in Rome. Comparisons are often drawn to the Roman Catholic Church, but the Church does not have the same willingness to tolerate major differences in theology between itself and the various other Christian sects that the Ecclesiarchy has regarding the differences among the various local strains of the Imperial Creed. A more accurate comparison would be to pagan Rome, which tolerated or ignored the various beliefs of its subject peoples, as long as they acknowledged the Emperor as the high priest of their pantheons in his role as Pontifex Maximus.
The "Imperial Cult" is just a blanket term which covers a multitude of belief systems which are compatible with the Imperial Creed and are tolerated by the Imperium, such as the Cult of the Redemption, Cult of Pure Form, a large variety of Death Cults (but not some of the more extreme ones), as well as a wide variety of Feral or Death world belief systems that have been modified by missionaries to incorporate the Emperor in some form.
The Ecclesiarchy is just the state church, which attempts to bring a level of standardization to how people worship the Emperor and to make relations between worlds relatively frictionless. Unfortunately, even this is a difficult task. The sheer size of the Imperium ensures that various sectors can still have their own variations on how the creed is interpreted, and may have different doctrines or venerate different canonised saints because no one system can control every form of belief that pops up across the Imperium. Needless to say, this translates into a lot of people calling each other heretics even when their interpretations of the Imperial Cult are equally valid as far as the Ecclesiarchy is concerned.
Because of this, the issue of Heresy can occasionally come about where different factions disagree with each other on what constitutes acceptable worship of the Emperor, though as per the original tenets of the Creed it takes a considerable level of deviation to truly count as abominable. Typically, this is determined either by the adoption of tolerance (or worse, outright subservience) towards xenos or the outright worship of other deities that are obviously not the Emperor, especially the Chaos Gods. The accusation of heresy still does a pretty good job of silencing debates or threatening people whose views are considered to be too far from the norm, even if they wouldn't actually be viewed as heretics.
However, it can and does go a bit further than this in day to day life. As the state religion, it does its best to cement itself as the only acceptable way to behave. So whereas the Emperor is the only true god, the High Lords of Terra are the Emperor's living agents, and the Ecclesiarchal priests are the speakers of His word --all of them are to be obeyed without question, no matter how suicidal or pointless their commands may be. Which basically translates as "Do as you are told by your superiors, or else. This generally involves: Working in horrible conditions until you die. If you don't want to do so and are stupid enough to express your views along those lines, you will quickly find out the hard way that the Imperium considers treason to be the same as heresy, since both of those involve refusing to acknowledge the supremacy of the Adeptus Terra.
The only major deviation allowed in the Imperium is the Cult Mechanicus of the Adeptus Mechanicus, thanks to the original Treaty of Mars allowing them to practice their own faith. Even so, this hasn't stopped tensions from popping up between the Mechanicus and the Ecclesiarchy. The commonly accepted compromise is that the Emperor represents the Machine God's physical avatar, the Omnissiah. While this compromise satisfies neither side, everyone goes along with it to keep the Imperium functioning. Even pious humans outside of the Adeptus Mechanicus, particularly Guardsmen, take the Machine Cult's beliefs seriously as their lives depend upon the technology they use.