When you click on a torrent file on a web site, it runs your torrent program, telling it to add that file to its download list. The torrent program is probably in your system tray (by the clock on the bottom right of the desktop).
If there's someone seeding the file, it'll start downloading. If not you'll just have to wait until someone is. (You're downloading files from people running torrent programs, not from a web site.)