Well, the whole internet is buzzing about the 'No panty day', 22 June, so New Europe crew decided to contribute to the celebration [in an informative and quasi-educational manner, not literally].
So, it is, apparently, the day for women not to wear panties or any undergarment in celebration of freedom [similar to the early days of protests against bras]. Or it might just be a joke, an online hoax. Regardless, it is fun and should be supported, promoted and encouraged, despite health and hygiene concerns.
Most likely inspiration for No Panty Day is No Pants day, which is a participatory holiday observed on the first Friday in June, when people spend their day not wearing any pants. The concept is based on breaking social taboos and seeing the reaction of people not aware of the event.
With the obvious appeal of No Panty Day, it would not be a surprise to see it becoming a tradition.