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 the island reappear, and other yōkai would attack the island only out of disgust for the existence of the hanyō children (especially to hide them from Kirinmaru and Zero) until the barrier recovers as the island disappear again. 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 jeweled 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 following of the conclusion of Inuyasha's battle with the Four War Gods, the island collapsed and disappeared forever.

Legacy
After the island disappeared and its time barrier faded, Kirinmaru has been awakened by his older sister Zero as the children will join the others in the outside world at the hidden village led by Shiori.

Trivia

 * Hōrai, or  as it is known in, was a rumored mystical land with two different origin stories. The movie depicts it based on.
 * In InuYasha the Movie 2: The Castle Beyond the Looking Glass, Hōraijima has the Jeweled Branch of Hōrai as of right in Lake Shōji to free Princess Kaguya from the Mirror of Life.