the great thing about bit torrent is that when you install it, you practically will never see it (save for when you click on the link to a torrent file). once you install the software, it basically acts as a p2p network that's a lot harder for anyone to trace. so your downloads are a lot safer from people snooping around (such as the riaa).
you use the program by going to a torrent search engine and downloading a small torrent file that will activate the bit torrent program. once activated it will start downloading and feeding off what you've downloaded to other users as well. there may only be a few complete files of whatever it is you're downloading and a ton of bits and pieces of those complete files that are floating around back and forth to users. so everyone is compiling a complete file by downloading small portions from all users currently downloading the main seeds.