This is a set of Samurai armour called O-Yoroi, or great armour. Samurai were warriors in feudal Japan, loyal to a shogun or daimyo. They were skilled in many fighting skills, especially the sword.
This is the oldest style of Samurai armour, made during the reign of the Tokugawa Shoguns. It is made from many scales of leather, laced together with cord then lacquered. This is much lighter and more flexible than iron which is only used under the left arm to give extra protection from swords and arrows. This armour would have been worn during battles, probably while on horseback, or at ceremonial events by lords or generals.
You can find the armour in the Asia section of our World Cultures gallery on the third floor of the museum.