Stronghold is a military building that protects units from enemy attacks. At each level, the amount of troops that can be protected increases. The Stronghold provides an increasing amount of Public Order. The soldiers that are not posted to the Wall (during defense) are in the Keep, so by placing your troops in the stronghold (and then assigning them special protection, they are then assigned to the keep), when they are assigned to the Keep they can be used in the courtyard battle for the Keep.