Celestial

A celestial (神人, shinjin, literally godlike person), also called an avatar or a giant, is a creature found in closed space, created when Haruhi Suzumiya's emotions become unbalanced.

Celestials are physically impossible, and could not exist in the real world. For instance, they are not strong enough to support their own weight. Haruhi releases her anger through them. It is the duty of an esper from 'the Agency' to remove the celestials, which they do by "slicing" them to bits with their powers. When this happens, closed space vanishes.

After meeting Sasaki, Haruhi began creating numerous areas of closed space again, complete with celestials.

Sasaki also has the ability to generate closed space, but hers never manifests celestials.

Beta Line
Following the meeting with Sasaki, Haruhi's celestials did not attack when they appeared in closed space, only acting in a daze. Koizumi believed their appearance was now triggered by Haruhi worrying about Yuki Nagato's unusual illness. The 'Agency' was still required to destroy them to remove the closed space, however.

Combined Timeline
Haruhi and Sasaki's closed spaces merged or "warred". At least one of Haruhi's celestials appeared, in time to rescue Kyon and Haruhi. They vanished, and Kyon briefly appeared in a distant future.

Trivia

 * Celestials briefly appear in episode one of The Melancholy of Haruhi-chan Suzumiya. When Kyon, while dreaming, discovers that Koizumi is not Mt. Fuji, he transforms into a celestial. Afterwards, he points towards the viewer and, in a menacing tone, says "Don't say anything to anyone about this" before turning back to normal.