Within the remit of the Privy Council and the Royal Court, Imperial High Command plays a mostly strategic role in the ordering of the gentry at war, doling out directives and coordinating between lord commanders in the field.
Each baronial commander, loyal to their count, is subject to the dictates of Imperial High Command, but IHC is subject to the order of the Royal Court, which is comprised of those same barons. Of course the King is within his rights to give direct orders to all, but it helps to have a system in which lord commanders feel they are ordering themselves about, somewhat insulating him from any resentment or blame.
During peacetime, the chambers of the Imperial High Command serve mostly as an extension of the castle. The main floor is converted into a ballroom, where many elaborate masquerades and invitational games are held.