The functional purpose of garter belts is to hold up ladies' stockings. They may also be used as a matter of style.
Garter belts began to replace girdles in the early to mid-20th century, as many women found girdles to be constraining and uncomfortable. In the later half of the century, garter belts were phased out in favor of pantyhose, whose name denotes its design: ladies' underwear combined with stockings.
Today, garter belts may be worn for stylistic or erotic purposes. Some women simply find the garter belt-stocking combination to be more comfortable than its contemporary counterpart, pantyhose, which may chafe, rub or slide down. However, garter belts are not always needed to keep stockings up, as many now come with elastic material that adheres to the body.