Lorule is a world that exists in parallel to Hyrule, and is first depicted in The Legend of Zelda: A Link Between Worlds. The world bears a visual resemblance to the Dark World of The Legend of Zelda: A Link to the Past, but the two are not the same. It is a separate world with its own Sacred Realm. Lorule is governed by Princess Hilda, an alternate world analogue to Zelda of Hyrule.
Lorule was once a peaceful and prosperous land, much like Hyrule, and like Hyrule, had its own Triforce. However, repeated struggles for the Triforce by those seeking to abuse its power to grant wishes led Hilda's ancestors to take the drastic step of destroying it. Done with good intentions, the act caused all of Lorule to fall into chaos and ruin.
With Lorule falling apart at the seams, Hilda discovers the existence of Hyrule and its own Triforce. She plots with Yuga to steal it away so that they might use its power to restore Lorule, but their plan is ultimately thwarted. Link and Zelda, pitying Hilda and the people of Lorule, use the power of the Triforce to make a wish; the restoration of Lorule's Triforce.
With the Lorule Triforce restored, the land quickly returns to vibrant life, giving the land and its people the chance to thrive like the land and people of Hyrule once again.