"Armory is where you can buy, improve and reserve Equipment. Better Armory allows you to buy more Equipment and upgrade them to a higher level."
Improving equipment doesn't actually upgrade the level of the equipment as the quote suggests. It only increases the stats. There is a google document with all information about items and their upgrade effects.
Opens the Armory menu that allows you to buy equipment
Opens the improvement panel that allows you to improve the stats of an item.
Opens the warehouse panel where you can manage unequiped equipment