The Armory is an important structure required to build certain units or structures. It focuses on generating a variety of resources and some Influence units.
The Armory allows for the construction of two influence units, being the Mod. Phantom and Mod. Gröditz. This sets it apart from most Resource Generation structures.
To upgrade the Manufactory or Barracks to Tier-3, an Armory is required. Some units are locked behind the Armory, such as the Sakata Mk-II, Jötunn or Eidolon units.
Although slightly slower at teching than Bank first, it is a viable solution as you gain quick access to the Mod. Phantom, Sakata Mk-II or Mod. Gröditz units. Furthermore it can expand the units you have at your disposal if you decide to construct the Multipurpose structure.
A neat build you can go is Hospital first, making meditecs and Armory second making Mod. Gröditz which is very strong in a 1v1 setting. Beware of those playing Communist or going Forge first which will break this strategy. The Mod. Phantom can also have its place early on if your foe is going Post.