The phrase "The Network" refers to the peer-to-peer network composed of all the computers and other devices that run an instance of the software architecture. In peer-to-peer networks, there is no distinction between clients and servers which means that the architecture of the peer software is all that's needed to completely define the whole network operation.
The peer-to-peer networks purpose is to provide a fault-tolerant foundation of tools on which to build larger organisational complexity in the form of the foundation ontology. Those tools include the ability to collaborate on knowledge, trade and self govern together in a way that is aligned with the common vision.
In terms of software architecture, the peer-to-peer networking aspect is at the foundation, because all other functionality is dependent on the ability to communicate amongst peers composing the network. Similarly the ability to form into groups, authenticate members identities and establish trustable private communications between them and of their stored data is also a common requirement at all scales of operation.
For this reason it makes sense to unify all of these fundamental communications oriented requirements into a single networking architecture. Of all these aspects, the most difficult to achieve is a solid means of trading, but this has recently been demonstrated successfully with the Bitcoin distributed currency. The next most difficult to achieve is decent decentralised authentication, but there are now also options for this, see the peer-to-peer article for details and related resources. The general idea is to extend the Bitcoin software (since it's the most difficult aspect of the networking layer) to include the less difficult and more available solutions of authentication and distributed storage.
Bitcoin is libre software and so is open and able to be extended to have new functionality incorporated in to it and could become completely multipurpose by adding additional information to coin blocks, for example NameCoin extends the network to provide a distributed DNS alternative. Similar things could be done to provide distributed authentication and a distributed ontology for shared knowledge and organisation.