In Klingon traditional history, Molor was a hated tyrant who ruled Qo'noS during the 9th century. He was said to be so strong that no man could oppose him but one: Kahless the Unforgettable. (TNG: "Firstborn")
Molor once sent five hundred warriors against the city of Qam-Chee. The city's garrison fled, leaving only Kahless and the Lady Lukara to make a stand in the Great Hall. Kahless and Lukara emerged victorious, after which they commenced the greatest romance in Klingon history. (DS9: "Looking for par'Mach in All the Wrong Places") Kahless and Lukara were also nearly killed by Molor's troops shortly after they were wed. This battle was commemorated by the use of ma'Stakas in the traditional Klingon wedding ceremony. (DS9: "You Are Cordially Invited")
The final confrontation between Molor and Kahless took place at the River Skral, which became the subject of a popular Klingon drinking song. (DS9: "The Way of the Warrior", VOY: "Barge of the Dead") Kahless slew Molor with the first bat'leth, which came to be known as the Sword of Kahless, and founded the Klingon Empire. (DS9: "The Sword of Kahless")
After Molor was slain, the shrines to him were abandoned and built over. The ones that survived were shielded to prevent detection. Followers of Molor continued to exist into the 23rd century; one custom among them was to pour an extra drink and light it on fire. (DIS: "Will You Take My Hand?")
According to the script for "Birthright, Part II", his name was pronounced as "moh-LOR". 
The exact time period in which Kahless, and therefore also Molor, lived has repeatedly been described with differing numbers. In DS9: "Looking for par'Mach in All the Wrong Places" taking place in 2373, Worf enthusiastically mentioned the events in Qam-Chee to have happened "a thousand years ago." This would appear to be somewhat of a contradiction as TNG: "Rightful Heir" stated that the monks on Boreth have been awaiting Kahless' return for fifteen centuries, i.e. five hundred years longer. Either Worf "rounded" the number of years in his enthusiasm, or Molor and Kahless were at least five hundred years old, which, while the maximum life span for Klingons had never been clearly defined, seemed to be without precedent. Another solution would be that Worf counted in Klingon years, as 2373 corresponded to the Year of Kahless 999. This would also be in accord with the Sword of Kahless being dated to an age of 1,400 years in DS9: "The Sword of Kahless". Furthermore, a scene cut from "Rightful Heir" had Data specify Kahless' death as 1,547 years ago, which would place it in 822 AD.