The Mission Day medal is awarded for attending Mission Day events. Check out the Ingress Live Events page to learn when and where Mission Day events are occurring.
Note that in order to get credit for attending, you must register on the official event page. If a Mission Day is not happening near where you live, contact your local tourism board and get them to collaborate to create one! Then fill out the application form.
The Mission Day medal was originally untiered, but Niantic converted it to a tiered medal, although at the time it did not contribute to agent leveling. After some initial issues which caused Niantic to revert the medal back to being untiered, it is now tiered and counts toward leveling.