In his youth before being crowned King, Randor was known as a fearless and great warrior who held the rank of Captain. At the end of The Great Unrest, Keldor and his evil forces brought confrontation to the Eternians. In a dramatic battle, Randor and Keldor clashed as enemies, with Randor eventually emerging victorious. Keldor left scarred, a victim of his own foul tactics; The acid he'd used as a weapon was deflected back into his own face, thus triggering his transformation in to Skeletor.
Impressed by his successes, Randor was crowned as the King of Eternia by the Council of Elders. King Randor appointing his own Eternian Council. The purpose of thisCouncil was to serve the world & guard against unseen and unknown evils, like Skeletor and his forces.
King Randor married the human test pilot Queen Marlena. Notably King Randor is the father of He-Man & She Ra. He is on good terms with his children, and is keen to instill great wisdom and morality within them. He is proud of them both, but often sought to inspire Prince Adam without realizing that Adam was also the great and brave He-Man. King Randor resides in the The Royal Palace of Eternia located in Eternos City.
He-man and the Masters Of The Universe (1983 Filmation):
Back in the original series, Randor was a stern, but wise king, his character often showed displeasure over his son Prince Adam as he did not show to much concern for the state of the kingdom, though in moments from time to time he is proud of his son at random acts of heroism that did not require the aid of He-Man. Little to no background was given about Randor's history except when he met his wife Marlena of Earth, and becoming King of Eternia after his father King Miro dissapeared. He would later, in the series, send his son to check on his twin sister who constantly fights the Horde on the world of Etheria.
He-Man and the Masters of the Universe (2002 Mike Young Productions):
In the 2002 revamp of the series much of the history of King Randor was defined and some changed. mainly himself becoming king was not the fault of his father being king and passing on the title, but of being dubbed king by the Council of Elders before their passing. Another change was brought up in order to bring continuity from the original comics, is that Keldor was made to be Randor's half brother. Both Randor and Keldor being decendants of the ancient King Greyskull, and would have access to the power that lies within Castle Greyskull.
Much of the character style had carried over from the previous series. Showing displeasure in his son often for not acting more like a royal. and not knowing the secret that Adam is He-Man. There was no mention of how he met Marlena or that she was even from Earth at all.