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BitTorrent trackers are like P2P servers.
When you open a .torrent file your BitTorrent client connects to a tracker from which it gets information on peers currently uploading and downloading files. It keeps track of the parts of the files that the users have. This information is very useful because it will give you an accurate number of Seeders and Leechers currently sharing using a particular torrent.
Most of the best torrent sites around now keep the pages updated with information from the tracker so users can know if a tracker is still alive (all parts are available) or is dead (not all parts are available, it is incomplete).
Development and research on "trackerless BitTorrent" continues as many see BitTorrent trackers as "centralised distribution points". This makes them an easy target for litigation if users of that tracker are sharing copyrighted content.