mid-13c., "fit for a king;" late 14c., "pertaining to a king," from Old French roial "royal, regal; splendid, magnificent" (12c., Modern French royal), from Latin regalis "of a king, kingly, royal, regal," from rex (genitive regis) "king," from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule."
Of institutions, "founded under the patronage of a sovereign" (c. 1500). The meaning "splendid, first-rate" is by 1853. The U.S. colloquial use as an emphasizer, "thorough, total" is attested from 1940s. Battle royal (1670s) preserves the French pattern of adjective after noun (as in attorney general); the sense of the adjective here is "on a grand scale" (compare pair-royal "three of a kind in cards or dice," c. 1600). Royal Oak was the name given to the tree in Boscobel in Shropshire after Charles II hid himself in it during flight from the Battle of Worcester in 1651. Sprigs of oak were worn to commemorate his restoration in 1660.
"royal person," c. 1400, from royal (adj.). Specifically "member of the royal family" from 1774, colloquial.