P2P, or peer-to-peer, is a general term that describes a network or form of communication where two devices communicate directly.
Usually when you visit a website, your browser sends a request to a server. The server then sends you back all the files (HTML, CSS, images, and so on) for your browser to render the website.
But if the server has a problem, you wouldn't be able to get all those files, and can't visit the site.
In a peer-to-peer network, a bunch of computers connect to each other and all act as small servers. If one computer in a peer-to-peer network goes offline, the other computers can fill in for it.
Several years ago, Spotify was one of the largest peer-to-peer networks. Back then, they leveraged P2P networking as a way to provide their service using their customer's bandwith. Now Spotify uses central servers that they control.
P2P can also be applied to other things like payments. In this context, it means that the payment gets sent directly to the other person. But the payment might still pass through a company's central servers, unlike a P2P network.
For example, if you send $20 to your friend with a P2P payments app like Venmo, they will receive the money instantly. Your friend can then transfer the money from Venmo to their bank account, or send it to someone else.
But if you use a traditional money wiring service, you will need your friend's bank information to send the money directly to their account. Also, the transfer might have fees, and take several days.