Hōraijima

was a place where yōkai and humans lived together in peace, resulting in many hanyō children. Since hanyō were unaccepted by the world, a barrier was put up to separate them from those who would shun them.

History
Every fifty years, the barrier would weaken, and other yōkai would attack the island only out of disgust for the existence of the hanyō children. Among them, were the Four War Gods. There was a battle, and to stop it, Lady Kanade, a priestess from the island, sealed the Four War God's powers into a jewelled box, and threw the box into the sacred Cauldron of Resonance. When she did this, her spirit was sealed into the Cauldron as well. The War Gods realized, that if they threw a hanyō child into the Cauldron, they could regain their power, little by little, though they were only able to do this every fifty years, when the barrier weakened. Inuyasha and Kikyō visited the island together at one point. They were ambushed by the Four War Gods, which resulted in Inuyasha being marked by them, and Kikyō having some of her blood stolen that would be used to create a replica of her.

During the story
Inuyasha and his friends traveled to Hōraijima to rescue the children after Ai was able to escape. When the Cauldron of Resonance, after being damaged by Inuyasha with Kongōsōha, was completely destroyed by Sesshōmaru with Sōryūha during his battle against Kyōra, the island collapsed and disappeared forever.

Trivia

 * Hōrai, or  as it is known in, was a rumored mystical land with two different origin stories. The movie depicts it based on.