The planet Eternia is theoretically governed by a worldwide monarchy with the ruling sovereign governing from the Royal Palace in the capital city of Eternos. The planetary monarch is a hereditary ruler, with King Randor the current sovereign, and Randor's son Prince Adam the heir to the throne.
History
King Jarod was the mythical first planetary monarch of Eternia, and founder of the planet's world government. Before Jarod's rise to power, various Ancient Ones apparently ruled various local portions of Eternia, in the era of the world's history known as Preternia. This probably occured several thousands of years ago.
More recently, around five hundred to eight hundred years before the present time, the period of the Great Wars occurs as the legitimate government of Eternia finds it's rule of the planet contested by the Snake Men under King Hiss. Toward the end of this period of three centuries, the Evil Horde under Hordak also invades Eternia apparently under orders from Horde Prime (this was centuries before Hordak and the Horde invade and rule the planet Etheria). Thanks to the leadership of King Grayskull, with some help from He-Ro, the traditional monarchy of Eternia regains nominal control of it's world. During these three centuries, King Hiss and his Snake Men occupied Eternos and the Royal Palace, and Castle Grayskull was first built during this three-century period in order to establish a new, temporary seat for the traditional monarch of Eternia and his government.
In practice, however, various cities, local kingdoms, regions, and factions exercise various degrees of independent autonomy, so political authority on Eternia is practically fragmented, much like with individual nations on the planet Earth. Randor, as planetary monarch, probably has to consult with various local and regional leaders before making laws. The Sorceress of Castle Grayskull (at first the former Queen Veena, then Kuduk Ungol, and finally Teela Na) is probably an occasional political advisor to whoever is the planetary ruler of Eternia.
Skeletor, with the aid of his Evil Warriors, has frequently tried to seize control of Eternia and become the de facto government of the planet. Skeletor was rumored to originally be named Keldor, the long-lost brother of Randor, and presumably as son of King Miro (like Randor), and used his family background to claim rulership of the planet.
Many years ago, early in Randor's reign, Hordak and the Evil Horde returned and again tried to seize control of Eternia and become the de facto planetary regime, but they were driven from Eternia and back to the planet Etheria (where the Horde still rules). During this time, Skeletor was a lieutenant of Hordak, and perhaps the Horde intended to rule Eternia with Skeletor as a puppet ruler.
In the 1983 Filmation series, Randor's father King Miro was also Eternia's planetary monarch, but be was kidnapped and went missing for many years, forcing Randor to become king.
In the 2002 series, King Grayskull, a distant ancestor of both Randor and Adam, had served as the planet's global ruler, but was mortally wounded, forcing his political advisors to become the semi-immortal Council of Elders and serve as Eternia's planetary government until the promotion of Randor to the long-vacant planetary throne.
This article/page assumes that descendants of King Grayskull and his wife Queen Veena served as planetary monarchs of Eternia, with the Council of Elders serving as advisors to the ruling monarch, and the Council members served as regents when the legitimate heir to the throne was underaged (still a child). When King Miro was kidnapped and disappeared for years, the Council of Elders selected Miro's son Randor as the new ruler of Eternia, because the Elders thought Randor's brother Keldor was too evil. Keldor then allied himself with Hordak and the Evil Horde, and the Horde used magic to turn Keldor into the present-day Skeletor. The Council of Elders soon disappeared from Eternia, but not before aiding Randor's government in defeating Skeletor, Hordak, and the Horde.
With the disappearance of the Council of Elders, the supposed incompetence of Prince Adam as heir to the throne and leadership of the planetary regime, and the continuing threat of Skeletor and his Evil Warriors, Teela Na, as current Sorceress of Grayskull, decided to give Adam the Sword of Power permitting him to transform into the superhuman He-Man. The so-called Heroic Warriors were also organized to aid Adam when he eventually asumes the Eternian throne.