Lorule

Lorule is a location in. It is a dark mirror of Hyrule, almost entirely congruous with the Dark World as featured in. The land once kept its own Triforce, an inverted counterpart of the one in Hyrule. Lorule is accessed via fissures that appeared in Hyrule, caused by the wizard Yuga. Most of Lorule's locations are isolated from each other by cliffs and large chasms. They must be reached by separate fissures found across Hyrule, which appear following a large quake.

The destruction of the Triforce
According to Princess Hilda, Lorule was once a land much like Hyrule. It possessed its own version of the Sacred Realm and its own incarnation of the Triforce. As was the case in Hyrule, the people of Lorule began to lust for their Triforce's limitless power. Many lives were lost as people warred over it. To end the strife, Hilda's ancestors decided to destroy their Triforce rather than seal it. However, without its Triforce, Lorule slowly began to crumble. As the generations went by, Lorule fell further and further into disrepair and edged closer to its doom.

A Link Between Worlds
In, Hilda, a princess of Lorule, learns of the existence of Hyrule and its Triforce. Desperate to save her people, she conceives an elaborate plan with Yuga to steal Hyrule's Triforce, knowing it would condemn the land to Lorule's fate.

Yuga then successfully captures each of the Seven Sages, including Princess Zelda (keeper of the Triforce of Wisdom), and, at Hilda's command, 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 fights Link until Hilda appears and uses her power to hold Yuga still so Link could escape the battle safely.

Link then rescues all the Sages from each of the dungeons in Lorule with Hilda as his guide and adquires the Triforce of Courage in order to face Yuga at Lorule Castle once more. This time, however, it is revealed that Hilda is the true villain, and she orders Yuga to get Link's Triforce of Courage. Once Link manages to defeat Yuga, Hilda orders Yuga to hand over the Triforce of Power, but he then betrays Hilda and takes 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.

Geography
The map of Lorule is extremely similar to the one of the Dark World, with a few notable changes, such as Lorule Castle standing where the Pyramid of Power stood, the Bomb Shop in the same location as the Vacant House, the Ice Ruins where the Turtle Rock was in the Dark World and the Turtle Rock from Lorule where the Ice Palace dungeon was, and some other differences including part of the rivers and land turning into a dark abyss.

Trivia

 * Lorule is an antonymic pun on "Hyrule." The first syllable, "Hy" (pronounced "high"), is exchanged with "Lo" (pronounced "low").
 * A remixed version of the original Dark World theme plays in Lorule.