If a network is described as peer-to-peer, or P2P, it means that all connected systems — i.e., nodes — share the same privileges. Cryptocurrency networks are peer-to-peer because all nodes are of equal authority, and transaction data is shared among nodes without reliance on coordination from a centralized server with additional privileges.
Anyone can join a peer-to-peer network. All they need is a device, a way to connect with other nodes (usually the internet) and a piece of software. As well as its use in cryptocurrencies, peer-to-peer networking was used in early file-sharing applications like Napster and LimeWire.