To be more precise on the English meanings of rein:
Noun: Reins are the straps that attach to the bridle, or headpiece, of a horse, which are held in the rider's hands.
Verb: To rein something in means to keep it in control, to limit it. It comes from the idea of pulling on the reins to slow a horse down. Snakesteuben 27 apr 2008, 04.40 (UTC)