The Composer is a device created by the Forerunners during the Forerunner-Flood War, and was intended to bridge the physical and digital realms. It was to create AI that inherited the personality of the composed individual, as an inorganic warrior could not be infected by the Flood. However, the personalities would fragment and attempts to restore them to biological form failed. The project was abandoned due to moral reasons, but the Didact ignored this and continued to compose his warriors into the Prometheans you're familiar with in Halo 4. The Prometheans lacked sufficient numbers to combat the Flood, so Didact composed a population of Humans on Omega Halo. Librarian found this amoral and confiscated the Composer, hiding it on Installation 03.

I could be wrong but I think it's that giant gray and orange ball he flies around in