A peer is another computer on the internet that you connect to and transfer data. Generally a peer does not have the complete file, otherwise it would be called a seed. Some people also refer to peers as leeches, to distinguish them from those generous folks who have completed their download and continue to leave the client running and act as a seed.
A computer that has a complete copy of a certain torrent. Once your client finishes downloading, it will remain open until you click the Finish button (or otherwise close it.) This is known as being a seed or seeding. You can also