Blue moon is not rare as it appears every after 2.5 years but Blue Moon on New Year’s Eve is, for it appears only after every 19-years. The last New Year Blue Moon appeared in 1990, the next will be on 2028. Hence, the colloquial term “once in a blue moon” referring to a rare event.
Blue Moon is definitely not blue: It is just a name in the same sense as a ‘hunter’s moon’ or a ‘harvest moon. The popular definition of blue moon came about after a writer for Sky & Telescope magazine in 1946 misinterpreted the Maine Farmer’s Almanac and labeled a blue moon as the second full moon in a month. In fact, the almanac defined a blue moon as the third full moon in a season with four full moons, not the usual three. Though Sky & Telescope corrected the error decades later, the definition caught on.[Source]
It does not change color: The moon will not change colors. According to the Farmers Almanac, the reference to the color “blue” in the expression reportedly came from times when ash from large forest fires or major volcanic eruptions propelled into the Earth’s atmosphere, thus causing the moon to take on a bluish tint. [Source]
The expression “Once in a Blue Moon”: It is a common way of saying not very often, but what exactly is a Blue Moon? According to the popular definition, it is the second Full Moon to occur in a single calendar month. The average interval between Full Moons is about 29.5 days, whilst the length of an average month is roughly 30.5 days. This makes it very unlikely that any given month will contain two Full Moons, though it does sometimes happen. On average, there will be 41 months that have two Full Moons in every century, so you could say that once in a Blue Moon actually means once every two-and-a-half years. [Source]
Possible symbolisms of the Blue Moon: There are probably at least six songs which use the term “blue moon” as a symbol of sadness and loneliness which is the opposite twist on the Vedic meaning. In a number of them the singer’s Moon turns to gold when he gets his love at the end of the song. Wonderful![Source]
It appears, however, that there are no significant astrological meaning of a Blue Moon except as being treated as an ordinary Full Moon.