Here is another nice early twentieth century illustration of two ladies horsing round in garters. It's an anonymous piece so we can't even guess the nationality of the artist but its likely to be French, given the period.
The word "garter" comes from the old french word gartier which itself originates from garet (probably a Celtic word), meaning the bend at the back of the leg. This refers to the top of the calf where garters were tied; that being the slimmest part of the leg. In modern French the word is Jarretière.
Garters would soon be replaced by suspender belts (garter belts in Amercia) for younger women and corsets with suspenders for older women until these too largely disappeared in the twenties. As skirts got shorter in this period stockings got longer, invariably going over the knee to the thigh; hence the need for suspenders.
In this picture we can see two types of garter: the traditional tie ones which were used from ancient times and were always tied below the knee and the elasticated ones which could be placed above the knee and were produced from 1820, when Englishman Thomas Hancock invented elasticated material.