(covers information from several alternate timelines)
The atmosphere of the planet created severe electromagnetic storms with charged particle precipitation that interfered with sensors and transporters. While the atmosphere was capable of supporting humanoid lifeforms, its electromagnetic characteristics had detrimental effects on their nervous systems. (TNG: "The Enemy")
In the alternate 2259, a mysterious wreckage was discovered on the mountainous surface of this planet. This event was reported in a news ticker, which was in a collection of graphics and video media that were seen on a powerwall in the offices of Christopher Pike and Alexander Marcus at Starfleet Headquarters. (Star Trek Into Darkness)
By 2366, the region had fallen under Federation control, where it was then located 0.5 light years from the Romulan Neutral Zone. It was also along the Barolian trade route with the Romulans. (TNG: "The Enemy", "Unification II")
That same year, the Romulan scout ship Pi crashed on this planet and the USS Enterprise-D was sent to investigate. The away team sent to the planet found the scout ship destroyed (deliberately, after it had crashed) and recovered a surviving crewmember. Unfortunately, Lieutenant Commander Geordi La Forge was trapped on the surface of the planet with another Romulan survivor, Centurion Bochra. Prolonged exposure of humanoids to the intense magnetic fields on Galorndon Core would result in synaptic breakdown. Bochra suffered from erratic metabolism and loss of sensation in his lower limbs, while La Forge became blind, even though his VISOR worked perfectly. (TNG: "The Enemy")
According to Admiral Alidar Jarok, this incident at Galorndon Core was common knowledge amongst Romulans. (TNG: "The Defector") However, he may have exaggerated how well-known the incident was, as he was covering up his true identity as an admiral.
In 2368, Galorndon Core was the rendezvous point where Ferengi arms dealer Omag delivered the stolen deflector array of the T'Pau to a Barolian freighter, which would later transfer it to the Romulans. In the search for the stolen deflectors, the USS Enterprise-D diverted to the planet from where it later detected three Romulan-controlled Vulcan ships, including the T'Pau, trying to covertly transport invasion troops across the Romulan Neutral Zone to Vulcan. (TNG: "Unification II")
"gal-OHRN-dan core" was the pronunciation for this planet's name from the script pronunciation guide for "Unification, Part II". 
For the remastered "Unification II", the appearance of Galorndon Core was corrected to match how it appeared in "The Enemy". 
In the computer game Star Trek Generations, Galorndon Core was a major Romulan base of operations and the site of a secret launch point for Soran's weapon. The base was headed by a Commander Tala, who appears twice in-game and who was helping Soran synthesize trilithium from Galorndon Core I.
The Pocket ENT novel To Brave the Storm depicts Galorndon Core as a xenoecological paradise in the 22nd century until the Earth-Romulan War. In a manner similar to the Romulan attack on Coridan Prime (as depicted in Beneath the Raptor's Wing), Romulan Commander Chulak led his ship into a suicidal attack against the Enterprise in 2157. He intentionally collided with the planet's surface at high warp, causing a destructive global cascade that rendered the planet uninhabitable.
In Star Trek Online, Galorndon Core is located in the Narendra Sector of the Tau Dewa Sector Block. A pod of Gekli have gotten lost in the system; the player must lead them past Hirogen hunting parties and back to fluidic space. In the Agents of Yesterday expansion mission, "The Core of the Matter", it is revealed that, like the depiction in To Brave the Storm, the planet was actually hospitable, if not a paradise of sorts. It was here that the Romulans and the Na'kuhl were in the makings of a partnership with the latter offering them a planet killer to become a great power. However, the Na'kuhl betrayed them and Chulak and the player character fights off the Na'kuhl. However, one Na'kuhl ship gets sucked into the machine, causing a chain reaction that sends the weapon spiraling to the planet, rendering it inhospitable.