In computer terms, a "peer" is an actual computer that exists on a network at the same level as another computer with similar access privileges. When you have two computers on a network, sharing files from each other's hard drives, it is known as a peer-to-peer relationship. This relationship has no shared resources on a server (as opposed to a client/server relationship, in which a workstation is specifically designated as a file server for allocating resources not available to client nodes). In technical terms, P2P is the ability of two or more computers to communicate on a network without a file server.
In popular culture, the "peer" in P2P refers to another person, someone else on the Internet with whom you share files. For example, music sharing is a popular P2P use of the net, as is photo, video and bookmark sharing.
Historical perspective: In 2009, the chairman of the House Committee on Oversight and Reform introduced a bill to ban the use of public peer-to-peer networks by federal agencies and employees due to sensitive documents being leaked over a file-sharing network. Some of the data that surfaced on P2P includes a confidential report on ethics investigations in Congress, location of a safe house for the Obama family, U.S. military documents and personally identifiable information, and diagrams of the President's Marine One helicopter. The Secure Federal File Sharing Act would prohibit the use of P2P software such as BitTorrent and LimeWire on government computers and networks.