Arm warmers are knitted "sleeves" worn on the arms. Sometimes worn by dancers to warm up their bodies before class, they have also become somewhat of a fashion item, appearing in the fall.
Arm warmers can also describe any glove-like clothing articles that lack finger coverings and/or were originally designed to keep wrists and lower arms warm.
Leg warmers are coverings for the lower legs, similar to socks but thicker and generally footless. Leg warmers are worn to keep the lower legs warm in colder weather. They can be tubular sleeves, long fabric wrappings, or simple fur or fabric tied around the calves.