Suspenders in US English, or braces in most variants of world English (and also sometimes in North America) are elastic fabric straps, run over the shoulders, that hold up trousers or a skirt. The entire strap of braces may be elasticated, or only the ends where the attachments are, with the majority part of the straps being of woven cloth with either a X-Back or Y-back crosspatch and leather end tabs.

Braces were at one time worn almost universally, due to the higher cut of late 19th and early 20th-century trousers which made wearing a belt less effective since it could not rest on the hips. Elasticated (and better-fitting) garments may also play a part. However, many business people, news casters and lawyers still wear suspenders, whether for image or comfort, and they are regarded as fashionable by most men's fashion experts in America (though not Britain). Braces are usually only acceptable items to wear at work if they are of high-quality, which normally means that they can be buttoned to trousers.

Suspenders in British English, or garters in North America are small straps or bands that hold up socks or stockings. For stockings, they are usually attached to a suspender belt or the bottom of a corset, and have special clips on their ends. Suspenders worn with stockings by women have a strong erotic appeal to many men. As with many items of female undergarments, they are sometimes items of fetish. For this reason they are sometimes worn by exotic dancers.

From Wikipedia