The Network was the creation of the Artificial Intelligence Deus to preserve his code and recompile it outside of the Renraku Arcology. It consists of over a thousand "Nodes", who are metahuman minds (as biological storage units) conditioned to accept his distributed code. Each Node is not consciously aware of the existence of Deus's code (except in certain exceptional situations) and seeks to jack into the Matrix at pre-set times to interact with other Nodes. The code was also distributed in a manner that Nodes could be expendable, and the copies of the code uploaded by the Nodes when they connect could also be implanted into new metahuman minds, turning them into Nodes (typically facilitated by Deus's "Whites").
In the final "download" to the Nodes (during the events of "Brainscan"), the AI Megaera inadvertently became twisted with Deus's code, and thus became rolled in with Deus into the Network. After the Nodes became dispersed among metahumanity, the Network became a covert war between Megaera-aligned Nodes and Deus-aligned Nodes, each side attempting to recompile its patron AI first, and assert dominance over the other Nodes.
Some Nodes, including the former servant of Deus known as Ronin, become independent from the Network, through the help of Ronin and the AI Mirage. These independent Nodes formed a loose coalition dedicated to seeking out other Nodes and freeing them from the Network.
This war came to a head in the events leading up to the Matrix Crash 2.0. Eventually, Deus "wins", and just after he recompiles himself, he heads to the East Coast Stock Exchange to take advantage of the processing power there. The actions that follow on November 2, 2064 precipitate the Matrix Crash.