A man-at-arms is a soldier — though actually, in history writing it is more special than “any fighter.” In the Middle Ages a man-at-arms was a trained fighting man, often in armour and often on a horse, paid to fight, not a farmer called up for one battle. The phrase is old. You meet it in stories of knights and old wars; today’s army just says soldier. The plural is men-at-arms. Arms here means weapons, not the two limbs on your body.