An elastic band worn around the upper arm. Originally, this was to allow for adjusting a sleeves length to better fit the wearer, or to hold up very long gloves that have a loose fit around the arm, but they have since become a decorative band on their own.
On Danbooru, arm garters usually look like Frilled Thigh Strap but are worn like an Armband, and are not used to hold up a sleeve. If they're worn over sleeves, then use the Sleeve Garter tag.