Strictly speaking, a peer to peer network is exactly as its name suggest - a group of computers sharing resources where no strict organisational structure exists.
In practical terms this means that any of the computers can access resources (files, etc) on any other computer provided the computer donating resources gives permission to do so.
The classic opposite of this is a 'client-server' approach, where a group of 'client' computers access resources residing on a central dedicated 'server' and do not interact with eachother.
For the record, the communications and hardware used (TCP, hubs, etc.) is irrelevant - the term refers only to the topology.