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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Definitions of realm from WordNet

realm (n.)
a domain in which something is dominant;
the rise of the realm of cotton in the south
Synonyms: kingdom / land
realm (n.)
the domain ruled by a king or queen;
Synonyms: kingdom
realm (n.)
a knowledge domain that you are interested in or are communicating about;
it was a limited realm of discourse
the realm of the occult
Synonyms: region