Rein

Reins are used to direct a horse when riding or driving. They are attached to a bridle's bit or noseband and are made of leather, nylon, or other materials. Reins are used to give subtle commands or cues—also known as rein aids—to ask for a turn, a slower speed, a halt, or to go backwards.

Other uses

The word "rein" is sometimes used incorrectly to refer to a lead rope or a longe line, neither of which are reins.
The idiom "rein in" means to hold back, slow down, control or limit, while in contrast "free rein" means to give or allow complete freedom, in action and decision, over something. Both are commonly misspelled as "reign in" and "free reign".
While reins are used on reindeer, the "rein-" in "reindeer" is not derived from the word "rein".