Question: What is peer-to-peer file sharing?
Peer-to-peer file sharing can be as simple as having file sharing between computers which are connected to a network switch or via ad-hoc wireless network connection at home. Please note the file sharing is performed with having any server involved (differ from sharing the files via server). By the way, Peer-to-peer is also commonly referred to P2P.
Nowadays this P2P file sharing has already evolved to enable file sharing on huge P2P network that involves millions of computers which are installed with P2P file sharing program (eMule, Kazaa, Bittorrent, etc). Check out this P2P file sharing article to learn more.