Latin for Whose Region, His Religion. Sometimes quoted as Cuius Regio Eius Et Religio (Whose Region, His Also Religion).
During the Protestant Reformation, the Cuius Regio rule was made into law by the Emperor of Austria, and probably by the rulers of several others European countries.
The rule was essentially based on the idea that the Emperor should not pass a law about religion, i.e., he did not want to decide whether the people of the Empire should remain Catholic or become Protestant. Instead, he passed the buck, so to speak, to the local feudal lords. Each lord was free to choose either religion, and his subjects then had to follow their lord's religion. The rule was the law for several centuries before it was abolished (and subjects were made free to choose their own religion).
This law makes an interesting tool for genealogy. Take, for example, the village of my ancestors, in North Central Slovakia, which was part of the Austrian Empire. The feudal family was the Szent Ivanyis. When Lord Szent Ivanyi became Lutheran, all of this subjects had to become Lutheran as well. Thus, the entire village, with the exception of one or two free families (not feudal, not subject) became Lutheran. This did not stop two young men three generations later to join the Jesuit order - so, the "conversion" was originally of the Rice Christian type. Of course, as is the case with Rice Christians everywhere, after a couple more generations, the subjects raised as Lutherans were "real" Lutherans. So, when the Szent Ivanyis became Catholic again (after the rule was abolished), the subjects remained Lutheran.
So, what does that have to do with genealogy? Well, knowing that, you can determine which family in the village of my ancestors was subject to the feudal lord, and which was free. Since my family is Catholic, for example, we know that our ancestors were free. But most of the village is Lutheran because freemen were an exception, not the rule.
Naturally, in the modern day, any such distintion (between subjects and freemen) no longer exists, but it is an interesting piece of family history, or genealogy.