Note: This is a rename of the module here http://drupal.org/project/contextual-flyout-links, which will be deprecated.
The contextual flyout links apply a new skin on the core drupal contextual edit links. The links are accessed through a left-aligned tab (right-aligned in RTL languages) that flys out to the left of the content. This updated positioning leaves the content in the block unobscured. When the flyout has insufficient space to the left (i.e. when the links collide with the edge of the viewport), the position of the flyout shifts to the inside of the block.