A full moon that hits twice in a calendar month. Given the cycle from full moon to full moon is about 29.5 days it doesn’t happen very often that this coincides so nicely. And February never has a blue moon.
I like this definition, but it is apparently a modification to the original definition which is a little more complicated. Given the 29.5 day cycle, most seasons of 3 months have 3 full moons. But every now and then, a season would come by, like Sep, Oct, Nov in the sketch, where there would be 4 full moons. The 3rd of these was known as a blue moon, or a seasonal blue moon. See why I like the modern definition?
Here’s a good article that explains the subtleties and history of blue moons.