Armor Stands are a type of furniture. Much like the weapon rack, the armor stand can be used to create a barracks. After being built, you may define the barracks dimensions. It can also be placed in a noble's room to appease them.
When used in a barracks designated for individual and squad equipment, dwarves will prefer to store their armor on stands instead of stockpiles. Doing so in concert with weapon racks will allow you to create centralized armories for your military.
Stockpile storage always takes priority over furniture, making armor stands all but useless for their practical purpose.
The current version of DFHack (r3) has scripts that repair armory behavior.