This form allows you to edit your bookmarks and associated tags or to change public/private status. 

Within My Bookmarks view, you have an Edit icon to the right of each bookmark.  Clicking this icon opens the Edit Bookmark form in line with your bookmark list pre-populated with the bookmark's existing information. you can make any changes and then click Save to update the bookmark. For more information on the fields in this form see the Add a Bookmark help page.

You can only Edit your own bookmarks; the Edit icon does not appear when you are in other views, such as "All Bookmarks", "Popular URLs" or another user's bookmarks view.