It opens you to the world of free information and stuff. Although that peer-to-peer file sharing is frowned upon by the government it is not technically illegal.
BitTorrent is a way of sharing/transferring files from one device to another. In simple terms it breaks up the files into tiny bits and sends them to the user downloading it. The more users sharing and seeding the file the faster you will get it. For information please see: http://en.wikipedia.org/wiki/BitTorrent