The Dream Corridor is a like a place that teleport you to one place to another at fast speed. It was opened the first time by Sara to get Lucia Nanami to the Indian Ocean Castle in the Indian Ocean for Seira's birth and it was opened the second time by Seira to allow Lucia, Hanon Hoshou, and Rina Toin to escapse from Mikeru.
In the anime it was only seen in episode 7 of Pure. It appeared like a one way passage of colorful lights that brought Lucia to the Indian Ocean at top speed. In the manga, it was much more detailed in chapter 28. The appeance in the manga is it is a long stairway that can only stay open for a short time before it close which is stated by Seira. It seems to appear that only Seira has this power since she was the one who create the magical staircase and at that time manifests helself as a substantial "spirit" form of her mermaid self to sacrefice herself to protect Lucia and the other mermaid princesses.