The Shitennou are a group within this organization consisting of the four most powerful members in it.
Decoranain's main purpose is to bring the Eternal Darkness to Earth. They have at least partially succeeded by the time the KiraDeco 5 arrive on Jewel Land. They further wish to obtain the Deco Stones so they can be corrupted with darkness and therefore clash with the heroic team frequently.
It was created by the Dark General as a way to get back at those who looked down on the nerd/otaku community; the Dark General envisioned his plan of covering the world in darkness while sparing nerds and otaku. The name of the organization in particular seems to spite Professor Decorisky, his ex-girlfriend who loved decoration, which he hated (note that 'nai' is a negative particle).