A physical representation of the gods.
The Gods is the term referring to the "collective human unconsciousness", C's World, which is the source of the individual identities for all humans, living and dead throughout the Code Geass Universe. Due to their human nature of not appearing equal, they are constantly in conflict with each other. Because of this, Charles zi Britannia, Marianne vi Britannia, C.C. and V.V. formed a contract with each other to activate the Ragnarök Connection via the Sword of Akasha to destroy the Gods. In Code Geass Akito The Exiled, the Dimensional Supervisor viewed humans as threats as they demand Gene Smilas to kill Shin Hyuga Shaing. She also believes that the Geass is a power that should not be give to humans as it can be abused.
Originally, references to the Gods were considered some sort of metaphor by people such as Cornelia, but that has become less likely as the series progressed. It is later revealed that they are a collective subconsciousness of all humans beings metempsychosed into the World of C, which is visually similar to Jupiter.
Charles intended to use the Sword of Akasha to trigger Ragnarök, that would destroy the Gods and once destroyed, every human that has ever existed, living or dead, will be united and exist as one mind, thereby creating what Charles deemed as true equality, as he saw ordinary human equality as inherently evil, if not non-existent. Lelouch, realizing that such a world would be stagnant and without a future, rejects this plan in favor of accepting reality. He then uses his fully-evolved Geass to give the Gods the request to deactivate and destroy Ragnarök, therefore causing the Gods to turn against his parents and dissolve them into nothing.
Despite this turn of events, it appears that the World of C can still influence and be influenced. As the World of C can be entered via the afterlife, all humans will inevitably go there when they die, as C.C. noted when killing Mao. Following his death, Lelouch was able to influence the World of C in order to say goodbye to Suzaku, Rivalz, Nunnally, Nina, and Kallen and will them various messages.