Mogh was a very influential figure in the Empire. He helped Huraga's House during their blood feud with the House of Duras. He was also a friend of Noggra and Lorgh. (DS9: "The Way of the Warrior", "Sons of Mogh"; TNG: "Sins of the Father", "Birthright, Part I")
In 2346, Mogh had suspected that another high-ranking Klingon, Ja'rod, was collaborating with the Romulans and was prompted to observe him. He followed Ja'rod to Khitomer, taking his wife, son Worf and Worf's nurse, Kahlest, with him. Not expecting a long trip, he left his younger son, Kurn, with Lorgh as he was only a year old. While there, Mogh was observed by the commander of the outpost as acting strangely. The Romulans then attacked the outpost, and he was killed along with his wife. Fortunately, Worf and Kahlest survived. (DS9: "The Way of the Warrior", "Sons of Mogh"; TNG: "Sins of the Father", "Birthright, Part I")
The fact that Ja'rod had betrayed the outpost's defenses did not come to light until 2366. As his House was very powerful at the time, the Klingon High Council decided to frame Mogh. Duras, son of Ja'rod subsequently made the allegation. Worf came to challenge it, however, having learned of the consequences of the truth being known, was forced to accept discommendation in order to protect the Empire. (TNG: "Sins of the Father", "The Drumhead")
This character was only mentioned in dialogue.
A deleted scene from DS9: "Tacking Into the Wind" saw Worf wish that Mogh was alive to see his son briefly be Chancellor of the Klingon Empire. (Star Trek: Deep Space Nine Companion - A Series Guide and Script Library)
It was widely assumed that Mogh was the son of Colonel Worf, but this was never confirmed on-screen. This assumption was briefly mentioned in the Star Trek Encyclopedia (3rd ed., p. 563). Promotional material for Star Trek VI: The Undiscovered Country, including interviews with Michael Dorn, stated that Dorn was playing Worf's grandfather in the movie.
While Mogh was never seen on camera, a trading card of the character was created for the Star Trek Customizable Card Game, using photo elements of both Worf and Kurn, combined together using Photoshop.
The Star Trek: The Lost Era novel The Art of the Impossible used the assumption that Mogh was the son of Colonel Worf, and stated that Worf was named after his recently deceased grandfather. The same novel also established that Mogh served as first officer under Captain K'mpec on the IKS Pu'Bekh. K'mpec noted that, while Mogh was a warrior and excellent with a disruptor pistol, he was terrible with a bat'leth. When K'mpec ascended to the Klingon High Council, Mogh became captain of the Pu'Bekh.