Limewire uses the Gnutella network, the largest p-p network on the web.
Torrents come from all over the web. LW can handle torrents, but it is slow and inefficient at doing so (and is banned from some torrent sites). However, it wouldn't hurt for you to try downloading a torrent via LW to see what it's about.

Start LW. Open your browser and do a (Google) search for a file, (a movie or song title plus the words 'free torrent'); your search results will guide you to a torrent site where you can find the file. Somewhere on that page should be, "Download this torrent". When you click on that you'll get a pop-up dialog (Open/Save); choose 'Open'. Go back to LW to see the torrent in your downloads window.

A few days ago I got a 700mb avi torrent from a public site in only 16 minutes via Vuze (without port forwarding!).
Yeah, torrents rock.