So far, it is known that the air of the Kraang's part of Dimension X is nitrogen mixed with sulfur and that it is very foggy. The water of Dimension X has hydrocarbon that can melt anything in the Dimension of Earth. For some reason, the water had no effect on April O'Neil when some of it was accidentally splashed on her. Later revealed to be because she's a human-Kraang hybrid.
It has also been confirmed that the Turtles will spend an episode in Dimension X in season 2.
In "Booyaka-Showdown, Part 2," Kraang Prime came to Earth from Dimension X in order to terraform it for the Kraang to live on.
In "Into Dimension X" it's revealed that time passes faster in Dimension X than on Earth, Mikey gets stuck in there for "months".