A P2P payment is a person-to-person payment: money sent by one individual to another, such as splitting a restaurant bill, paying rent to a flatmate or sending money to a relative. The main entry describes how these payments work and the services that offer them. P2P is the common abbreviation, read either as person-to-person or as peer-to-peer.
The two readings can cause confusion. In payments, both mean a transfer between private individuals as opposed to a payment to a business or by a government. In technology and crypto, peer-to-peer describes a network in which participants deal directly with one another without a central intermediary. Most P2P payment apps are not peer-to-peer in that second sense: a bank or payment company sits in the middle and moves the money on its own ledger or over a bank rail.
A P2P payment is almost always a push payment started by the sender, identified by the recipient's phone number, email address or username instead of account details, and it is the typical send money feature in a banking or mobile payment app. Because such transfers are fast and hard to reverse, they are a frequent channel for authorized push payment fraud.