To be a little more specific, when you are logged in, the edit link appears to help you edit the page you are viewing, just in case it needs editing. It is a fast way to edit. It was developed long before there was an Admin Bar with the Edit option there.
When you are logged out, and to the rest of the world not logged into your specific site as a contributor, the edit link is gone. It is invisible to everyone that does not have permission to edit that post.