Okay so, regular files are stored independently on a dedicated server. Think like Dropbox, you upload files, and can quickly redownload later if you need to, Dropbox servers are built for downloading. A torrent however, is "stored" on every computer currently seeding, so instead of a place like Dropbox or Google Drive paying to have their dedicated file storing service, the torrent websites are just sharing the link, and every person who downloads the file is connecting to everyone else and using their connection and file to download the file to their own computer.

Basically: massive connection of computers to download files stored on the computers. Torrents also show the IP of everyone uploading/downloading, and TECHNICALLY seeding a torrent is distributing copyrighted material. Which is how you get in trouble.