The use of the phrase "blue moon" in the English language has been traced back as far as the 1500s, when the Oxford English dictionary cites it as an example of saying something patently absurd. The phrase didn't acquire its more contemporary meaning related to rarity until the 1800s.
(This excellent article from Sky & Telescope magazine sorts most of this out, especially the interesting bit of ephemera surrounding its own contributions to confusing the issue from an astronomical perspective.)
As far as astronomers are concerned, a blue moon simply refers to the second full moon that occurs occasionally in a given month—a relative rarity, to be sure, but one that is the work of our calendars, and not on the order of the or a lunar eclipse.
WSJ: So blue moons are nothing special? And they’re not even that rare?
Tyson: Let me tell you something about full moons: kids don’t care about full moons. They’ll play in a full moon, no worries at all. They only get scared of magic or werewolves from stupid adults and their stupid adult stories. Scientifically illiterate adults are the problem. And the weather in New Jersey, y’know, if it’s overcast or something.
It takes the moon 29.5 days to wax and wane from full to new to full again. With the exception of February, months are longer than that, meaning that once in a while the timing works out so there are two full moons in one month.
The most kismet you are likely to find tonight? It's the same day that family and friends will hold a private memorial service for Neil Armstrong; the late astronaut was the first man to walk on the moon.