An Approval is a box that, once opened, gives a Blessing of a [Path], which is a charm that doubles the path points earned for 3 days. The charms only take effect after the character has talked to his or her mentor.
Each path has its own approval box containing the path's Blessing charm. A character can only use an approval that belongs to his or her path. If you're a Guardian, you can only use "Approval of a Guardian".
Approvals do not stack with each other and they do not affect boosters.