c. 1300, reine, "strap of a bridle," attached to it on either side of the head, by which the rider or driver restrains and guides the animal, from Old French rene, resne "reins, bridle strap, laces" (Modern French rêne), probably from Vulgar Latin *retina "a bond, check," a back-formation from Latin retinere "hold back" (see retain). Compare Latin retinaculum "a tether, halter, rein."
The figurative extension of reins to "guidance, means of controlling; control, check, restraint" is by mid-14c. Hence many expressions, originally from horse-management: Hold the reins "wield power" (early 15c.); take the reins "assume the power of guidance or government" (1610s). To give something free rein also is originally of horses; to give (a horse) the reins (1620s) is to allow it free motion.
c. 1300, reinen, "tie (a horse), tether," a sense now obsolete, from rein (n.). From early 15c. as "to pull on the bridle with the reins," to restrain or guide the horse, hence the figurative extension to "put a check on, restrain, control," recorded by 1580s. Related: Reined; reining. To rein up "halt" (1550s) is an image of pulling up on the reins to make a horse halt or back.