It's time for some clarification for anyone that hasn't encountered this holiday before.
In Japan and some other Asian nations Valentine's Day is essentially split into two holidays in contrast to how things are in the west. Valentine's day is the day when women will give gifts to men. White Day is essentially the answer to the gifts given on Valentine's Day where one month later a man will reciprocate with a gift of their own back.
For more detail you can read up on the holiday at https://en.wikipedia.org/wiki/White_Day