“The average time the Moon takes to complete a cycle of phases is 29.5 days. So all months but February can host a second full Moon, if the timing is right. We call these “Blue Moons” and we get one on Friday, August 31. Chances of a full Moon on the first of a month is about 1 in 30, so you’d expect a Blue Moon every 30 months or so — about once every 2.5 years. Not rare. So when the cosmically literate want to reference something that’s uncommon, they **never** say ‘Once in a Blue Moon’.” – Neil deGrasse Tyson, Astrophysicist, Director of the Hayden Planetarium
Of course, a “blue moon” is still used colloquially to mean “a rare event”, as in the phrase “once in a blue moon”. The Farmer’s Almanac defines a Blue Moon as an extra full moon that occurs in a season. One season normally has three full moons, so if a season has four the extra one (actually the third, not the fourth ) was named the blue moon.