"P2P" is an abbreviation for "peer-to-peer," a term in computer programming that refers to the ability of computers to share files directly, without the need of a central server. The idea is that hardware and software can only communicate with "peers" that have the same connection. Small offices often have file sharing among computers that do not have a central server connecting them.
The original designers of DARPA computers had this in mind when they designed programs, software and networks on computers that could communicate through phone lines in the 1960s. Data was sent directly from one computer to another, which denoted the original design of early Internet computers, before server-based Internet protocols became the norm.
Peer-to-peer networks allow computers to borrow processing power from another computer, copy files and documents, and send messages. Each computer in a P2P system can be configured with each user's preferences. For instance, one computer may allow files to be copied but not edited, whereas another computer may allow someone on a remote terminal to read and write files. Instead of one computer processing a large file all at once, several computers on the same P2P network use less processing power and less time to complete a large task by breaking the task down into smaller elements for each computer.