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, you can collaborate with Niantic to create one! Read the guidelines, then fill out this form to apply. Note that the odds of your Mission Day being approved by Niantic go up if you secure a local partner, such as a tourism board, museum, etc.
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.