In the olden days, people counted their months my moons - the words still sound alike, even. There was a storm moon, a harvest moon, a wolf moon, when the wolves came closest to townships in winter, etc.
These moons where what they lived by. They were easy to see even if you didn't keep track of each and every day. To peasants back than a day was not important, nor was keeping track of years, but knowing each year and each moon was vital for harvest.
The name of the moon always referred to the "full moon" in a way, but the "month" lasted from one new moon until the next. So to speak the life of one moon from birth to death.
Now that poses a problem if you also live by the cycle of the sun. The sun takes 365.25 days before it reaches the same point again. The moon takes 29.5 days to renew. That makes it 12 moon cycles in a year which adds up to 354 days. Those lack 11.25 days before the end of the year, or 11 days each year and 12 days in every 4th year.
When you look into a calendar you'll find each year has 12 full moons, only some have 13. This 13th moon then occurs within the last 12 days of the year. And that's - surprise surprise - the time between Yule December 21st and the 1st of January.
This is where the word "between the years" and the 12 days of Yule or Xmas originate. This is also how it happened that January 1st (the 12th day after Yule) long ago became the first day of the new year.
If there was a 13th moon in a year, people called it the Blue Moon. It was *not* each second full moon in any given month! What does the moon have to do with our man-made months anyway? Our current months from January to December where invented by some king or other and have nothing to do with the moon phases any more.
On the other hand the 'real' Blue Moon (like we have one in December 2001) was considered highly unlucky by our ancestors, together with the time it occurred in. Believe it or not, my mother still tells me you should not do your laundry between the years.
The 12 days of Xmas are now the days between December 24th and January 6th, the beginning of the christian year. This has to do with the shift Yule underwent with the upraise of christianity.
So, there is your scientific explanation for Blue Moons as seen by our ancestors. If you consider them lucky or unlucky or nothing at all is up to you of course - or your high priestess. But before she tells you to dance naked around an oak on the 30th of November just because it's the second full moon in this month, think, ask some questions, and wear a sweater.
If you want to know the phase of the moon at a given date and time, please check out this applet