Origins
Reign entered English in the 13th century from Old French 'reigne' (kingdom, rule, authority), which descended from Latin 'rēgnum' (royal power, kingdom, dominion). The Latin noun derived from 'rēx' (king), from 'regere' (to rule, to guide), from PIE *h₃reǵ- (to move in a straight line, to direct, to rule).
The word's journey through French shaped its modern English form in important ways. The Latin 'g' in 'rēgnum' stopped being pronounced as French evolved, but the spelling preserved a trace of it. English inherited this silent 'g' in the form 'reign,' creating one of the language's many spelling-pronunciation mismatches. The word is a perfect homophone of 'rain' (from Old English 'regn,' a Germanic weather word) and 'rein' (from Old French 'rene,' a horse strap from Latin 'retinēre,' to hold back).
This homophony has practical consequences. The expression 'free rein' — meaning to allow unrestricted freedom, from the horsemanship practice of loosening the reins — is frequently misspelled as 'free reign.' The error is understandable: the image of unrestricted royal power maps neatly onto the meaning. But the original metaphor involves horses, not kings.
Latin Roots
In Latin, 'rēgnum' encompassed both the act of ruling and the territory ruled. This dual sense carried into English: 'reign' can mean the period during which a sovereign holds power ('the reign of Elizabeth II') or the act of ruling itself ('she reigned for seventy years'). The word has also extended beyond literal monarchy: a champion 'reigns supreme,' and we speak of a 'reign of terror.'
The phrase 'Reign of Terror' refers specifically to the period from September 1793 to July 1794 during the French Revolution, when the Committee of Public Safety under Robespierre executed thousands of perceived enemies of the Republic. The term has since become a general expression for any period of violent, unchecked authority.
The related word 'interregnum' (from Latin 'interrēgnum,' literally 'between reigns') refers to the gap between two successive rulers. The most famous English interregnum lasted from 1649 to 1660, between the execution of Charles I and the restoration of Charles II, during which England was governed as a Commonwealth and then a Protectorate under Oliver Cromwell.
Proto-Indo-European Roots
The 'regere' family permeates English. 'Royal' (from 'rēgālis,' kingly), 'regal' (same source, direct Latin borrowing), 'regent' (one who rules in another's stead), 'regime' (a system of rule), 'regulate' (to control by rule), 'rector' (a director), and 'region' (a territory under rule) all descend from the same PIE root. Even 'right' (from Old English 'riht,' straight, just) is a Germanic cognate, preserving the original sense of straightness that underlies the entire family.