These clients use the BitTorrent protocol, a peer-to-peer file-sharing protocol that's used to distribute large amounts of data. Rather than downloading a file from a single source, BitTorrent allows users to join a "swarm" of hosts that can upload and download files in pieces.
BitTorrent (the company) is just one of many that offers the client software to handle BitTorrent (the protocol).
The company has released additional statistics about the usage of its clients: There are over 20 million daily active users, and the client is downloaded an average of 400,000 times per day. The software is available in 52 languages, and the clients check in from over 220 countries every day.
Although the P2P protocol has long been associated with digital piracy, BitTorrent made a number of agreements with content creators such as Pioneer One and the Yes Men in order to distribute their works.