The Precursors were a race preceding and mythologized by the Forerunners, being theoretical "Transsentient" beings, having the ability to travel among galaxies and accelerate the evolution of intelligent life. The Precursors reached a level of technological sophistication that dwarfed even the Forerunners, capable of creating nearly invulnerable artifacts that could withstand the stresses of a planet's mantle or even connect two planets.
The Forerunners considered the Precursors to be Tier 0 on their Technological Achievement scale, transsentient beings similar to gods, able to travel across entire galaxies (and possibly between universes as star roads leave multiversal residues when exiting out of FTL) and responsible for accelerating the evolution of sentient life. As the Forerunners had no examples of civilizations with technological accomplishment greater than themselves - with the exception of the Precursors - this is a theoretical ceiling.
They can travel intergalactic distances and accelerate evolution of intelligent life. All that is known about the Precursors' appearance is based upon the prisoner at Charum Hakkor, the last known Precursor. Precursors were massive in size; the mold encapsulating the Prisoner of Charum Hakkor outlined a being approximately fifteen meters tall and eleven meters wide. They were vaguely humanoid, with four arms, two legs and an insectoid head. A long, segmented "tail" was attached to the base of the skull, tipped with a meter-long barb. Each hand had three fingers and a central opposable thumb. The face of a Precursor has been likened to that of a eurypterid, or "sea scorpion." Their heads were flattened, with oval compound eyes and (presumably) mandibles or similar mouth parts.
Precursors are stated to be able to mutate into any many different organisms of different complexity, sometimes some individuals regressed into being landlocked in worlds before increasing in complexity when they choose. The being at Charum Hakkor was also stated by the ISO Didact to be a gravemind, possibly hinting that the primordial was some ancient form of flood and not a Precursor at all. Though, the flood is actually the corrupt and tortured bodies of the Precursors themselves. Being Transsentient they were able to be both corporeal or non corporeal at any given time to enrich the Universes "Living time".
More information regarding the Precursors can be found at these links: http://halo.wikia.com/wiki/Precursor