The "Hide Links" link on your site is used to hide and unhide the editing options of your easysite.
After you click "Hide Links" all the links that are used to add, edit and delete items will be hidden. In this mode, the site will look similar to how a visitor would see the site.
This cleans up the interface for those times when you're just reviewing what's already on your site.
This is how the list of albums looks when your showing links.
This is the same list when your hiding links.