The Continuum is a league of civilizations whose area of influence spans many solar systems, perhaps the bulk of the Milky Way galaxy. Their earliest direct encounter with earth was their performing the action of metamorphosing several human astronauts into unique transmutations. The humans, dubbed The Apollo Eleven, became emissaries of a sort. The Continuum also sent a special representation called (for lack of a better name) L.G.M.. Their overall mission was to determine whether humanity was mature enough to join the Continuum, or if deemed a threat to stellar interests, take actions to elimination them.
The Incarnate, was a special kind of being, formed by a joining of the Apollo Eleven into a single, powerful meta-entity. His most important task was to serve as the emissary for judging humankind's fate. He first appeared in the winter of 1977.
Xosmos serves as a voice for the group, or did as of 1982. In that year the Apollo Eleven were trying to postpone the judgement of Earth, and prevent the Sol System from experiencing the same oblivion as the four solar systems of Deneb 13.
They are likely on a higher echelon than the Galactic Council, which might just be concerned with more local matters. Starwoman, whose race the K'ntarians are a driving force on the Council, went to the Continuum on our behalf in 1982 when the Continuum passed judgement on Earth.