"Once in a blue moon..." It's a cliche that we hear often. It's meaning is that something only happens once in a while.
A blue moon may not live up to the cliche's name, though. A blue moon happens every 2.7 years.
The cycle of lunar phases takes 29.53 days. That's less than a month (unless you're talking about February).
One year has 365.26 days.
A little math shows that more than 12 lunar cycles happen each year, but there are only 12 months in each year.
365.26 days per year / 29.53 days per lunar cycle = 12.37 lunar cycles per year
The extra .37 gets added year after year.
It works out, then, that an extra full moon (the 13th in a year) occurs every two or three years.
This extra full moon, then, becomes the "blue moon" for the month that it occurs.