Ishmael describes what a whale line is in the next part.  It is made of hemp, and it is a rope connected to the harpoon at one end, but dangles free at the other end.  This is so it can be tied to the other boats' lines.  This rope is laid out throughout the ship and 'whizzes' out when a whale darts with it stuck in him, making it very dangerous for the harpooners.  When you think about it, whaling seems to be a very dangerous job.