If they connect to the torrent file that you're downloading from, they can tell:
What IP's are downloading
How much they've downloaded
So, all they have to do is find the torrent, which is pretty easy. BitTorrent works through a tracker, which your computer connects to regularly. These trackers usually have links to the torrent files they are tracking. They could then find your ISP and send them (or you) letters and lawsuits.