I had always understood a blue moon to be the second full moon in any calendar month, but I am evidently not entirely correct.
I came across a really interesting article on space.com today about the origins of the term blue moon. Before it meant what I always thought it meant* it meant the third full moon in a season that has four full moons.
Originally the full moons of each season were called the early[season] moon, the mid[season] moon and the late[season] moon. However, in 1937, because of a misunderstanding in Sky and Telescope magazine that went viral, we now understand a blue moon to be the second in a month with two.**
Merriam-Webster’s definitions include only the modern celestial meaning (though, admittedly, the first definition is the colloquial definition rarely.) The Etymology dictionary addresses, albeit awkwardly, the quarterly definition and notes that the modern definition is incorrect.
For more, go here and read the article, because it’s really interesting.
*I can’t help a Princess Bride reference here and say “I do not think it means what you think it means.”
**An interesting tidbit for the next time you’re at pub quiz…a blue moon will occur seven times in a 19 year cycle.