When you turn off your computer, all your active applications are terminated too. Putting your computer to Hibernate mode on the other hand will pause all active programs. There will be no data transfer in or out of your computer during this.
Either way, the torrent you are downloading will not be erased though. It will resume when you activate or run your torrent client again. What you can also do is to set the torrent client you are using to shutdown the computer after completing the download. I'm using the light, free and easy to use uTorrent (micro Torrent) and it has this option. I suppose other torrent clients have this too.