Etymology
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realm (n.)

c. 1300, reaume, "kingdom, domain under a sovereign, royal jurisdiction," from Old French reaume, laterrealme, variants (in part by influence of Old French reial "regal," from Latin  regalis) of roiaume "kingdom."

This is possibly from a Gallo-Romance *regiminem, "formed as an accusative on Latin regimen government, rule" [Barnhart; see regimen], or from or as if from Vulgar Latin *regalimen "a kingdom," from Latin regalis [Century Dictionary, OED; see regal], or some combination of the two [Klein]. Realty and royalty tended to come out of Old French in similar forms, and roylty in Middle English also could be spelled realty. (14c., from Old French reaute, realte).

The modern spelling predominates from c. 1600. Transferred or figurative sense of "sphere of activity; area of power, influence, or operation" is from late 14c.

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*reg- 

Proto-Indo-European root meaning "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule."

It forms all or part of: abrogate; address; adroit; Alaric; alert; anorectic; anorexia; arrogant; arrogate; bishopric; correct; corvee; derecho; derogate; derogatory; Dietrich; direct; dress; eldritch; erect; ergo; Eric; Frederick; Henry; incorrigible; interregnum; interrogate; maharajah; Maratha; prerogative; prorogue; rack (n.1) "frame with bars;" rail (n.1) "horizontal bar passing from one post or support to another;" Raj; rajah; rake (n.1) "toothed tool for drawing or scraping things together;" rake (n.2) "debauchee; idle, dissolute person;" rakish; rank (adj.) "corrupt, loathsome, foul;" real (n.) "small Spanish silver coin;" realm; reck; reckless; reckon; rectangle; rectify; rectilinear; rectitude; recto; recto-; rector; rectum; regal; regent; regicide; regime; regimen; regiment; region; regular; regulate; Regulus; Reich; reign; resurgent; rex; rich; right; Risorgimento; rogation; royal; rule; sord; source; subrogate; subrogation; surge; surrogate; viceroy.

It is the hypothetical source of/evidence for its existence is provided by:

Sanskrit raj- "a king, a leader," rjyati "he stretches himself," riag "torture" (by racking); Avestan razeyeiti "directs," raštva- "directed, arranged, straight;" Persian rahst "right, correct;" Latin regere "to rule, direct, lead, govern," rex (genitive regis) "king," rectus "right, correct;" Greek oregein "to reach, extend;" Old Irish ri, Gaelic righ "a king," Gaulish -rix "a king" (in personal names, such as Vircingetorix), Old Irish rigim "to stretch out;" Gothic reiks "a leader," raihts "straight, right;" Lithuanian raižytis "to stretch oneself;" Old English rice "kingdom," -ric "king," rice "rich, powerful," riht "correct;" Gothic raihts, Old High German recht, Old Swedish reht, Old Norse rettr "correct."

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fandom (n.)
"the realm of avid enthusiasts," 1903, from fan (n.2) + -dom.
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catdom (n.)

"cats generally, the realm of cats," 1853, from cat (n.) + -dom.

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gangland (n.)
"the criminal underworld; the realm of gangsters," 1912, from gang (n.) + land (n.).
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wonderland (n.)
"imaginary realm," 1787, from wonder (n.) + land (n.).
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heavens (n.)
"realm of the heavenly bodies," 1670s, from heaven.
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satrap (n.)
late 14c., "governor of a province of ancient Persia," from Latin satrapes, from Greek satrapes, from Old Persian xšathrapavan-, literally "guardian of the realm," from xšathra- "realm, province" (related to xšayathiya "king," cognate with Sanskrit kshatra; see shah) + pavan- "guardian," from PIE root *pa- "to feed; to guard, protect." Related: Satrapy.
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Peru 

ancient realm in northwestern South America, later a Spanish viceroyalty, since 1821 an independent republic, from Spanish Peru, said to be from Quechua (Inca) pelu "river." Related: Peruvian.

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biosphere (n.)

"Earth's surface and lower atmosphere as the realm of living organisms," 1899, from or modeled on German Biosphäre (1875), which was coined by German geologist Eduard Suess; see bio- + sphere.

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