The Shogunate or known in Japanese as a bakufu (幕府) (the latter of which literally means "an office in the tent", and originally meant "the house of a general"), was a body present within the government of the Empire of the Rising Sun and consisted of its top leaders. It was presided over by the Emperor. The Emperor also has the power to chose another individual (usually a member of the Royal Family) to preside over the shogunate should the Emperor feel it necessary. The Emperor also has the authority to elect individuals who have proven themselves through their service to the Empire, to the Shogunate itself.
This administrative body is entrusted with far-reaching powers. Its members are representatives from all corners of the Empire. Thus, the Empire of the Rising Sun can be called an oligarchy of sorts, although the Emperor is a powerful presence and presumably have ultimate authority over the Shogunate and the Empire.
The full Shogunate meet periodically at the Shogunate Headquarters in Tokyo to discuss matters of Imperial interests. At the time of such a conference, all the civilian and military leaders of the Empire will be together at one place, a situation exploited by the Allied forces launching a surprise assault against Tokyo when the Shogunates were meeting inside their HQ. As a result almost all of the Empire's leaders was either captured or killed when the Shogunate Headquarters was surrounded and subsequently destroyed, effectively knocking the Empire out of the war.
World War III
In the Imperial persepective (see main article World War III), when the Empire discovered that Soviet forces used time travel to escape their fate and the subsequent timeline brought about the rise of the Empire of the Rising Sun, the Emperor was dismayed at the thought of there being no divine destiny if time itself was malleable. He thus gave command of the Shogunate to his son, Crown Prince Tatsu. After the last of the Allies and the Soviets finally pacified, the Commander responsible was granted the title of Supreme Shogun, apparently the highest military rank within the Shogunate.
In the Command & Conquer: Red Alert 3: Uprising Era, the Shogunate was disbanded by the Allied occupiers of Japan. Some former Shogunate leaders, including acting Head of State Tatsu, opted to work for the Allies. Others fled into the countryside and rebelled against Tatsu's authority. During the Allied campaign, three rebelled shogunates were arrested as in the Imperial campaign, Tatsu brought along Kenji Tenzai (one of the rebellers) to help the Imperial Commander attack the Soviets in Vladivostok and Sakhalin Island.
Behind the scenes
The term bakufu originally meant the dwelling and household of a shogun, but in time it came to be generally used for the system of government of a feudal military dictatorship, exercised in the name of the shogun; and this is the meaning that has been adopted into English through the term "shogunate."
The shogunate system was originally established under the Kamakura shogunate by Minamoto no Yoritomo. Although theoretically the state, and therefore the Emperor, held ownership of all land of Japan, the system had some feudal elements, with lesser territorial lords pledging their allegiance to greater ones. Samurai were rewarded for their loyalty with land, which was in turn, on the liege lord's permission, handed down and divided among their sons. The hierarchy that held this system of government together was reinforced by close ties of loyalty between samurai and their subordinates.
Each shogunate was dynamic, not static. Power was constantly shifting and authority was often ambiguous. The study of the ebbs and flows in this complex history continues to occupy the attention of scholars. Each shogunate encountered competition. Sources of competition included the Emperor and the court aristocracy, the remnants of the Imperial governmental systems, the shōen system, the great temples and shrines, the shugo and the jitō, the kokujin and early modern daimyo. Each shogunate reflected the necessity of new ways of balancing the changing requirements of central and regional authorities.
For more details about Shogunates in the real world, follow the link.