The medical term for arms and legs is "extremities." The two pairs of extremities on a human being are distinguished by position, with the arms being called the superior or upper extremities, and the legs being called the inferior or lower extremities.
The extremities may also be called limbs or appendages. The uppermost part of the arm and the lowermost part of the leg have special medical names as well. The section of the arm between the shoulder and elbow is called the brachium, while the section of the leg between the knee and the ankle is called the crus. Sometimes "arm" is used as a synonym for the brachium in technical usage, but it is easily confused with the popular usage of "arm" for the entire limb.