While a ‘back cinch’ traditionally refers to the leather strap attaching the saddle around a horse’s back, on a pair of jeans it is used to tighten the waistband. Also known as a martingale, it consists of a denim strap and a buckle that’s placed on the yoke of the jean.
Back cinches were the common way for jeans wearer to tighten the waist before widespread use of belts. Jeans with a back cinch also referred to as ‘buckle back’ and most jeans manufacturers abandoned the back cinch in 1942. With renewed interest in vintage-styled looks, cinch backs have returned on modern jeans.
Source: Nouvelle de Nîmes Nº 5: The Denim Dictionary and Denimhunters