Torrent is a form of P2P. It is different opposed to users using a built in search feature in their P2P software they load a .TORRENT file obtained from a "tracker" site. This file contains hash data and the trackers URL. The torrent software hooks up to the tracker and uploaders and downloaders get hooked up.
On the bit torrent network there are Peers (as it is PeertoPeer filesharing. Peers can be divided into leechers and seeders. A leecher is a person who is downloading the file, at the same time peers can download and upload (unlike other P2P protocols/software). Once a person is done downloading they stop downloading and continue uploading. This is called Seeding in which the peer is now a seed(er).
See the P2P article as it explains more about filesharing in general and legal issues.