Dude just go to wikipedia and search for "file sharing" or p2p and you should get informed about torrents. But heres my interpretation. When people download files off of torrent sites (movies, music, photos, etc), they need an application to download the file (azureus, limewire, kazaa, etc). The .torrent file is usually very small and only tells the application certain things it needs to know in order to download the file (i.e. the tracker
http://www.mp3powa.com:2710/announce). Usually the torrent site will tell you the "health" of the torrent, which are leechers/seeders. "Leechers" are the people still downloading the file, while "Seeders" are people who have successfully downloaded the file and are sharing it. The more seeders/leechers the better and probably more faster your file will download. That is why it is called "file sharing" or "peer-to-peer" because you are downloading from many sources, as opposed to downloading straight from one server.
P2P is totally legal and is used very much among open source communities. But downloading of copyright material is illegal. Most of the world downloads copyright material and it is highly unlikely that you will get caught.
I myself use Azuerues as my application, they recently made it more user friendly too. I am starting to download HD content for my movies, either HDTV, Blu-ray, or HD-DVD rips. It takes up oh so much space on my computer, but the picture quality is amazing.