P2P means Peer to Peer. This can be translated as communication between equals. This means the computers communicated trhough P2P communicate with each other without a central server intervening.
When communicating through a P2P server, your computer functions as both client and server. It asks for data to other computers (Client) and also provides data to other computers (Server).
There are lost of applications using this kind of commmunication, among them a frequent use is file sharing, as: Azureus, Kazaa Lite, eMule, etc. It is also highly known the voice comunication application Skype, also used on P2P communication.