Peer-to-peer is a type of network design where all devices support roughly equivalent capabilities. Peer-to-peer networking (also known simply as peer networking) is in contrast to client/server networking, where certain devices have responsibility for providing or "serving" network information and other devices consume or otherwise act as "clients" of those servers.
Peer-to-peer networking is most common on small LANs, particularly Windows home networks. Peer networking on the Internet gained widespread popularity thanks to file sharing services like Napster. However, many of these file sharing services, including Napster, actually integrate both peer and client/server networking design. Technically, these are called hybrid networks.