A "seeder" is a person who has completely downloaded a file or files using BitTorrent, and is uploading those files to others. A "leecher" has not yet finished downloading the file or files, and is thus both downloading from seeders and other leechers and uploading the portion of the file or files he has downloaded to other leechers.
The ratio of seeders to leechers in a BitTorrent swarm (the set of people uploading and downloading a particular torrent) is an important indicator of the torrent's overall health. If a torrent has few seeders and many leechers, file transfer speeds are slow, as few people have the whole file. If there are no seeders at all, the torrent may die if there is not a full copy of the file between the remaining leechers. On the other hand, if there are many seeders and few leechers, file transfer speeds are fast and the torrent is not in danger of dying. Because of this, private torrent trackers often mandate that users upload a certain percentage of the data that they download, or risk being banned from the tracker. Even if a tracker does not mandate an upload/download ratio, it is advisable to upload as much as one downloads to maintain torrent health.