Theocracy

"If we must have a tyrant a robber baron is far better than an inquisitor. The baron’s cruelty may sometimes sleep, his cupidity at some point may be sated; and since he dimly knows he is doing wrong he may possibly repent. But the inquisitor who mistakes his own cruelty and lust of power and fear for the voice of Heaven will torment us infinitely more because he torments us with the approval of his own conscience and his better impulses appear to him as temptations."

– C.S Lewis on why Theocratic Rule would really suck in practice

A theocracy is a form of government in which religious authority dictates secular authority. Basically, priests and nobles are one in the same; there may be secular authorities below them, but ultimate power lies in the hands of the clergy alone.

Religious Rule in Antiquity

Flavius Josephus is credited with the term, where Against Apion was casting about to explain the (idealised) Jewish religio-political system to Greek-speakers. For him (and keep in mind this guy was a famous traitor) YHWH is sovereign, and His people follow Divine Torah. Day-to-day operations default to the interpreters of the Law. This means if there's a king all he does is law-enforcement and war, and if there's a priesthood they're just caretakers of the Temple.

In practice the term gets expanded beyond that. Josephus professed rabbinical Judaism and, being extremely educated and intelligent, interpreted this with a heavy dose of Hellenistic rationalism. (It certainly didn't hurt Josephus' case, since he was a traitor, that all this allowed that Vespasian Caesar be G-d's secular Messiah over his fellow Jews.) In antiquity most religions had a serious byline in mumbo-jumbo, and if they could fool the people with their tricks, they could claim to be speaking for whatever God resided in that particular temple. So usually "theocracy" is applied to hierocracy: rule by priests.

In settings where divine magic is a thing, and in our own Bronze Age there was little distinction between "magic" and "miracle", theocracies can overlap with the concept of magocracy. After all, surely the most powerful wielders of divine magic are those closest to the divine, and if your entire leadership structure is based on proximity to the divine, those are the people with the best claim to the throne.

This isn't necessarily always true, but usually, theocracies where power and authority aren't tied to magical power despite divine magic being a thing are supposed to come off as hypocritical villains - see the infamous Cult of Entropy in the Forgotten Realms.

Theocracies tend to be either monotheistic - holding to the belief that is only a single god, or else they are henotheistic -- don't worry if you've never heard that one, it's pretty obscure outside of religious studies. Basically, henotheists acknowledge that there are multiple gods, but hold a single god as either supreme over those other gods (as in Vodun) or otherwise as the only god worth worshipping for whatever reason (as in LDS).

Polytheism actually doesn't tend to work out so well for theocracies. Dirty little secret: ancient temples doubled as banks. (Guess who had all the scribes and accountants?) When Sumerian citystates accumulated too much wealth into Temple A, Temple B would cry foul. The usual end was for the major temples to unite into a cartel. Then the commoners would cry foul and a tyrant would arise, like Urukagina, declaring the annulment of debts (amargi). Josephus would say these temple-cartels weren't true theocracies but pff.

Which isn't to say that monopoly Temple rule works out all wonderful either. These are subject to outsiders, usually disgruntled insiders by origin, setting themselves up as "prophets" with a better claim to Divine favour than the insiders do. The examples in Islam are innumerable; we can recommend Ibn Khaldun for details.

/tg/-cracies

Before Warhammer, Dungeons & Dragons offered quite a few theocracies. Oddly the first-published in the Greyhawk setting was under said setting: the Drow, in GenCon XI. These fallen elves are a henotheistic theocracy of both types; they qualify as the first type in that whilst the various deities of the Dark Seldarine are acknowledged as existing, but all are seen as subordinate to Lolth; and they qualify as the second type in that, well, nobody can deny the existence of gods like Moradin or Pelor when there are priests and priestesses casting bless and flame strike in their name. It is the Priestesses of the Spider Queen who hold power absolute, and no matter how powerful the nobles may be, that power is always inferior to that wielded by the priestesses. A half decade later Greyhawk's overworld got published with the Theocracy of the Pale and the See of Medegia.

Mystara got Hule, implicitly the same merger of Platonism with caliphal Islam which Khomeini was running in Iran, which the Desert Nomad series REALLY hammered into us with the third of that trilogy. Eberron has Thrane, the site of The Silver Flame. Thrane is unusual here because the existence of the Silver Flame is, unlike the other faiths of Eberron, provable and Thrane does not have a monopoly on worship of The Flame (even though the physical Flame is in its borders) causing it to fight other worshipers in the Last War.

The Imperium of Man, conversely, and counterintuitively to normies, is not a theocracy; because whilst the Ecclesiarchy is a power-bloc within the government, they are not technically the ultimate authority of the Imperium. It does have theocratic elements, but isn't completely ruled over by the priests of the God-Emperor. It is ruled over by the actual God-Emperor himself . There is no name for such a type of government, because for obvious reasons we haven't had to invent one... yet (there technically is a term: thearchy (rule by God/a god/gods). But this term has never been put into actual practice for obvious reasons). Ignoring that, since the God-Emperor is basically a deified near-corpse on (what everyone else thinks is) life-support, the actual day-to-day running of the Imperium is handled by an enormous bureaucracy descended from the council that reported to him when he was more fully functional.