The Hellforge is a magical forge found in the deepest pit of the Realm of Destruction—the realm's sole source of creation, yet devoted to the forging of weapons that would only be used to destroy. The Hellforge holds many anvils where Hell's most powerful weapons were created, among them the Anvil of Annihilation.
During the Great Conflict, the archangel Izual led an assault on the Hellforge, in an attempt to prevent the creation of the demonblade, Shadowfang. However, he was overcome by the demonic legions.
Long after Izual's fall, a group of heroes made their own assault on the Hellforge. It was their intent to use the Anvil of Annihilation to destroy Mephisto's soulstone and after retrieving it, Diablo's as well. In both counts they were successful, and the soulstones were destroyed and their contained spirits supposedly banished to the Black Abyss.
The Hellforge appears in Act IV of Diablo II and is protected by an Overlord called Hephasto the Armorer, who holds the Hellforge Hammer required to smash the Soulstone. During Diablo II, your hero completes a quest named Mephisto's Soulstone, where he/she smashes Mephisto's soulstone using the Hellforge and the Hammer.
However, you do not need to have Mephisto's soulstone in your personal inventory. Either this may be a bug, or somehow, Tyrael's magic allows him to teleport the soulstone directly to the Hellforge when you are there and ready to use it. All you really need is to wield the Hellforge Hammer, and whether it's on your inventory or in your stash, you will still be able to complete the soulstone-smashing quest with it. Nevertheless, the soulstone is found to have vanished once you reopen your Stash.
When the soulstone is destroyed it gives several perfect and flawless gems as well as a potentially high-level rune. It is common to offer the reward for characters' Hellforge quest in exchange for a rush.
The possible runes vary by difficulty:
Note that each possible rune has an equal chance to drop (1:11), meaning the odds you'll get a Gul in Hell difficulty are exactly the same as the odds you'll only get a Hel.