The BitTorrent file-sharing system consists of the following components:
- a group of clients (also referred to as "peers", since they upload as well as download), referred to as a "torrent swarm"
- a server for tracking client activity (mainly so that clients can find each other), called the "torrent tracker"
- a set of files being torrented, which start out at one location and are gradually disseminated throughout the swarm
- a .torrent file (one per file set) which specifies the names of the files being shared and a checksum for each file chunk
This is an explanation of how BitTorrent generally works in practice.
One person decides they want to distribute a set of files over the internet. They collect those files on their computer and then create a .torrent file describing the files (names, sizes, and a checksum for each "chunk" of each file) in the set. The .torrent file is typically fairly small, ranging from a few tens of kilobytes to maybe half a megabyte for a really large fileset containing many gigabytes.
They then upload the .torrent file to a torrent tracking server, typically via the server's attached web site (there are many of these), and describes the torrent so that others can find it via the web site's search capability. The torrent tracking web site then announces the availability of the torrent and includes its description in searches. (At some point the torrent file also has information added to it giving the location of the torrent tracking server.)
Anyone who wants those files then downloads the torrent file and loads it in a torrent peer application; the very first client software was called BitTorrent, but there are now many others (and most of them work better).
As each peer downloads the files, it also offers for upload whatever chunks it has downloaded so far. This is the primary virtue of the BitTorrent system: it distributes the bandwidth load across all users. Another incidental virtue is that it also distributes the copyright violation liability and keeps the "server" from actually handling any of the copyrighted data; this is discussed below.
As the torrent tracking sites and servers do not actually host or copy the copyrighted information itself, they were generally immune from legal prosecution during the technology's early days; stakeholders in the copyright enforcement business spent more effort targeting individual users of torrent software, with emphasis on the fact that these users are illegally offering copyrighted files for download (possibly because this sounds more incriminating than just "illegally downloading copyrighted files").
In the early 2010s, however, many well-known torrent sites went down due to apparent legal attacks from the copyright industry. (More research is needed.)