Peer-to-peer networking (P2P) is an application that runs on a personal computer and shares files with other users across the Internet. P2P networks work by connecting individual computers together to share files instead of having to go through a central server.
From : www.netalert.net.au/01990-Glossary.asp

A peer-to-peer (or P2P) computer network is a network that relies on computing power at the edges (ends) of a connection rather than in the network itself. P2P networks are used for sharing content like audio, video, data or anything in digital format. P2P network can also mean grid computing.
From en.wikipedia.org/wiki/P2P