Traditionally, panties were worn underneath garters and lingerie is still advertised and photographed in this way in catalogues and on websites. However, some people wear panties over the garters. If the panties are reasonably tight, this pins the garters to the body, making going to the bathroom or erotic play easier.
A garter is also a means of stocking support. It is slipped over the top of the stocking to hold the stocking by essentially clamping it to the leg. These are the garters typically seen at weddings.
A garter belt is a piece of lingerie worn around the waist like a belt which has "suspenders" or "stays" that clip to the tops of the stockings to hold them in place.