Strictly speaking, a blue moon is the third full moon in a season that has four. This happens seven times every nineteen years – approximately once every two or three years.
According to Wikipedia, the misconception that it's the second full moon in a calendar month arose from an article published in 1946 in Sky & Telescope – a monthly magazine for American amateur astronomers. The author attempted to work out how the editors of the Maine Farmers' Almanac calculated the occurrence of a blue moon. It turned out that he didn't have enough copies of the Almanac to show the full story, but his erroneous conclusion gained enough credence to make it the most popular explanation ever since. It no doubt helped that it's somewhat simpler than the correct version.
Wikipedia also tells us that the earliest known reference to a blue moon is in a pamphlet published in 1528 by "two converted Greenwich friars". The pamphlet attacks Roman Catholic clergy, and Cardinal Thomas Wolsey in particular, claiming that "If they say the moon is blue, we must believe that it is true".
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