Blue Moon
Ask anybody today and a blue moon is the second full moon in a calendar month. That definition entered the language through a 1946 article in Sky & Telescope, whose author was reading the Maine Farmers' Almanac and misunderstood its rule. The almanac's blue moon was the third full moon in a season that contained four — a seasonal bookkeeping device, not a calendar one. The simpler wrong version spread through a radio programme and a board game question, and by the time Sky & Telescope printed a correction in 1999 it had been the popular meaning for half a century. Both are now in use, which is why two sources can disagree about whether a given month has one.
Where the name comes from
Neither definition has anything to do with colour, and a full moon is never blue by arithmetic. The Moon does occasionally look blue, and that has a real cause: particles of a particular size scatter red light and let blue through. It happened after Krakatoa in 1883, when the Moon was reported blue or green for months, and again over Canada in 1950 after enormous forest fires in Alberta.
Also called the second full moon in a calendar month, the third of four in a season.
Sky & Telescope, 'What's a Blue Moon?' (1999 correction of its own 1946 article) (opens in a new tab)