You might have used the term ‘once in a blue Moon‘ before – a colloquial phrase to suggest that something is very rare. But just how rare, depends on your definition.

In astronomy there are two definitions of a Blue Moon; both are a type of Full Moon. Here Blue Moon is defined as either (1) the third full Moon of an astronomical season with four full Moons or (2) the second full Moon in a calendar month.

Such a Blue Moon as defined in (2) will next occur on Friday, 31-Jul-2015 at 10:43am UTC (7:43am ADT) – July/2015 therefore has two full moons; on the 1st (11:20pm ADT) and 31st of July (7:43am ADT).

The next Blue Moon according to (1) will occur on 21-May-2016. This then will be the third full moon in the spring season/2016 which will have four full moons (23-Mar/22-Apr/21-May/20-Jun-2016).

Now note that summer solstice in 2016 is on 20-Jun too. So how would that days full moon still be attributed to spring? This is because astronomically the 20-Jun-2016 full moon occurs at 8:02am ADT (11:02 UTC) and summer solstice does not happen (technically) until 7:35pm ADT (22:35 UTC) on the same day – roughly 11.5 hours later.

Contrary to popular belief, a Blue Moon is not actually blue in color – if it looks blue, however, it is a very rare sight. The Moon, full or any other phase, can appear blue when the atmosphere is filled with dust or smoke particles of a certain size; slightly wider than 0.7 micron, for instance after a dust storm or a volcanic eruption.
Eruptions like on Mt. Krakatoa, Indonesia (1883), El Chichon, Mexico (1983), Mt. St. Helens (1980) and Mount Pinatubo (1991) are all known to have caused blue moons.

Red Moons on the other hand – which are much more common – can be caused by other sizes of dust particles or by Total Lunar Eclipses.

Btw: About once every 19 years, the month of February does not have a full Moon. The years when this happens, also have two full Moons in two different months. This phenomenon will occur next in 2018 (when January and March will have two full moons each).

©2015 timeanddate.com
For the Wiki definition see here.