A group of users all sharing the same file is called a "swarm".
The core innovation of BitTorrent is . When a user wants to share a large file, the protocol breaks it into hundreds or thousands of small "pieces".
Traditionally, a central server called a "tracker" helps peers find each other. Modern clients also use Distributed Hash Tables (DHT) , which allow for a "trackerless" experience by letting peers find each other directly. Key Benefits of the Protocol BitTorrent - ScienceDirect.com
A "seed" is a user who has 100% of the file and continues to upload it to others. A "leecher" (or peer) is a user who is currently downloading the file but also sharing the pieces they have already received with others in the swarm.
BitTorrent is a decentralized communications protocol designed for peer-to-peer (P2P) file sharing. Unlike traditional downloads where a single server sends a file to many users, BitTorrent allows users to download pieces of a file from each other simultaneously, making it one of the most efficient methods for distributing large amounts of data across the internet. How BitTorrent Works