An Etymological Dictionary of Astronomy and Astrophysics

The second full moon in a calendar month. For a blue moon to occur, the first of the full moons must appear at or near the beginning of the month so that the second will fall within the same month. Full moons are separated by 29 days, while most months are 30 or 31 days long; so it is possible to fit two full moons in a single month. This happens every two and a half years, on average.

See also: The folkloric term blue Moon for the calendrical event is new, and apparently goes back to the Maine Farmers’ Almanac for 1937. But its original meaning in that work was the third full Moon in a season when there were four full Moons in that season. Some have related the term to the much older English expression moon is blue, which goes back to a couplet from 1528, interpreting it as “something that occurs rarely.”
However in that poem the expression had a meaning of “something that was absurd.” Alternatively, the term blue Moon may have been borrowed from the Chinese lunar calendar particularly in its usage among American Chinese community. In fact in that calendar when there are two full Moons in a month they use the term “blue Moon” and add a thirteenth intercalary month. → blue; → moon.