The name "blue moon" is merely folklore. Every three years, or so, there are two full moons in a month. (one on August 31 this year!).
Normally, there is a full moon 12 times a year.But "time" accumulates; which is why we have Leap Years. Then a full moon will appear twice in the same month.
I don't think it has any more magical significance than any other full moon.Although it may have done in ancient times. Don't forget, the moon's orbit takes 29 days, and there are many months with 31 days! So it is bound to happen every so often.