Lorule

Lorule is a location in. It is similar to the Dark World in that it is a dark, twisted mirror of Hyrule, and an inverted counterpart of the Triforce is found there. Visually, it is reminiscent of the Dark World, is similarly accessed via portals in Hyrule, and similarly contains some of its important areas where such areas were located in the Light World/Hyrule. However, unlike the Dark World, most of its locations are cut off from each other due to cliffs and large chasms and must be reached via separate portals in Hyrule, while the Dark World only had this trait for a few locations.

History
According to Princess Hilda, Lorule was once a land very much like Hyrule, complete with its own version of the Sacred Realm and its own incarnation of the Triforce, though in their world the Triforce was inverted to reflect its counterpart in Hyrule. As was the case in Hyrule, the people of Lorule began to lust for their Triforce's limitless power, and many lives were lost as people warred over it. To put an end to this, Hilda's ancestors decided that their Triforce had become too much trouble, but rather than seal it away, they opted to completely destroy their Triforce. While this was done with the best of intentions, this inadvertently caused Lorule to begin to crumble without the protection of their Triforce to hold it together. As the generations went by, Lorule fell further and further into disrepair and edged closer to its doom. Eventually, Hilda learned of the existence of Hyrule, the twin to her kingdom, and its own Triforce. Desperate to save her people from doom, she conceived a plan with Yuga to steal Hyrule's Triforce and use it to restore Lorule, even if this meant Hyrule losing its Triforce and thus condemning it to destruction as Lorule was.

Yuga successfully captures all of the Seven Sages, including Princess Zelda (keeper of the Triforce of Wisdom), and, at Hilda's behest, eventually breaks the seal placed on Ganon's spirit so as to access the Triforce of Power he held. Fusing with the Demon King, Yuga fought Link but failed to defeat him, and in the midst of battle, betrayed Hilda and took from her the Triforce of Wisdom she had taken from Zelda as he had no interest in saving her crumbling kingdom and would rather remake it in his image. Energized by the Triforce of Power and the Triforce of Wisdom, Yuga once again battled Link in an attempt to take the Triforce of Courage from him, but was ultimately defeated by the young hero wielding the Master Sword. This released Hilda, who though shaken was ready to once again attempt to take the Triforce pieces from Link and Zelda, until Ravio, Link's Lorulean counterpart who had once served Princess Hilda before fleeing in cowardice, returns to talk sense into the princess and help her see that stealing Hyrule's Triforce would bring out the worst in Lorule. Finally brought to her senses, Hilda realizes her error and resolves to do the right thing alongside Ravio to return Link, Zelda, and their Triforce to their homeland, even if this meant the end of their own world. The pair took Link and Zelda to their world's version of the Sacred Realm and sent them home from there.

Once home again in their own world, Link and Zelda resolve to make a wish upon the reformed Triforce together to grant Princess Hilda and her world a parting gift. Back in Lorule's Sacred Realm, as Hilda and Ravio turn to leave and watch the dimming of their world, both are shocked and overjoyed to see their world's Triforce restored as a result of the wish Link and Zelda made upon Hyrule's Triforce, thus saving and restoring Lorule.

Trivia

 * Lorule gets its name from a combination of "Low" and "Hyrule;" the "lo" comes from the first syllable of "Hyrule" sounding like "high."
 * A remixed version of the original Dark World theme plays in Lorule.