The God Machine was the universal construct that Yahweh formed around the entirety of his Creation. He wished for his Creation to be autonomous, running on its own rules and replicating itself as it needed in order to preserve what He had made. When Yahweh abandoned his Creation, however, the Machine's programming went wild and began to act upon protocols that it understood to be logical. Lucifer Morningstar, assisted by the Brotherhood in Violence, placed Elaine upon the vacated Seat of the Word - but the God Machine reacted by rejecting its new sovereign. It continues, to this day, to search for Yahweh.
Cogs in the Machine are agents of the God Machine. Aidan Clayce, the Voidseeker, has been fighting a long and lonely battle against the Machine in the hopes that destroying it will liberate all of humanity. Finding means to either destroy the Machine completely or program it "properly" has become even more important in this Darkest Vigil, for Hunters have just discovered that the Machine is being manipulated by the Watcher in the Dark. The Watcher has had the Machine hit the "kill switch" on the Fifth World, thus summoning Nyx to the realms.