Could someone please...

when you download a .torrent files from somewhere, like thepiratebay.org or mininova.com your downloading a torrent file, which is just basically a MD5 sum and instructions on how to download/piece together the file you want.

then you open that .torrent file in bittorrent, which reads the MD5 sum and instuctions and finds other people who have bittorent open and that file loaded into it. People who have the entire file are called seeders, people who are downloading part of it are called leechers. You would be a leecher until you get the entire file.
bittorrent will find other people with that file, and download small pieces of data from each of them, which by splitting up the file and downloading from many sources, usually increases the speed drastically. It also allow you to shut your computer down and pick up the download where you left off, when it restarts

Hope that helps!