The Turtle Lair is the main home of the Ninja Turtles and their sensei Splinter. This was the second home that was featured in the 2003 show, the first being a more ordinary sewer that they spent the first decade and a half of their lives in. When this lair was rendered unsafe and unstable by the Mousers, Splinter proposed the move to the new lair, which he had found while he was escaping from the Mousers.
This new lair was much larger and more comfortable than their old one, with a bedroom for each of the brothers, an area for Donatello's lab, a large living area with an entertainment system, and an outlet into the ocean. It also had a mysterious, hidden elevator that led to the upper world, which none of the Turtles initially could explain.
The structure was eventually revealed to be of Y'Lyntian origin, perhaps as some kind of outpost of the Underground City.