From my article on Examiner.com:
A "blue moon" usually just means that a second full moon appears in the same month. This special event happens every two or three years (on average about every 2.7154 years) when there is an extra full moon. The phrase has been around a long time, well over 400 years, but during that time its meaning has shifted. There are six different meanings which have been carried by the term, and at least four of them are still current today.
The origin seems to be when the Clergy was calculating the dates for Lent and Easter they identified the Lent Moon. But when the moon's timing was too early, they named an earlier moon as a "betrayer moon" (belewe moon), when the Lent moon came at its expected time.
So in folklore, they gave each moon a name according to its time of year. A moon which came too early had no folk name – and was called a blue moon – bringing the correct seasonal timings for future moons.
The Farmers' Almanac defined blue moon as an extra full moon that occurred in a season; one season was normally three full moons. If a season had four full moons, then the third full moon was named a blue moon.
Mankind has always looked to heavenly events for meaning and direction. The new age spiritual movements have actually given the New Year's blue moon extra meaning...you can read my hub for this side of the answer.