A blue moon, generally, refers to a second full moon which occurs in the space of a single calendar month, although there are several varying definitions. Generally speaking, a blue moon occurs every several years, because of the way in which the Earth year, the calendar month, and the lunar rotation almost, but not quite, align perfectly: a month lasts 30 or 31 days, while the moon takes 29.5 days to orbit the Earth and complete a full cycle of new moon, waxing moon, full moon, waning moon, back to new moon again.
The last blue moon occurred on December 31, 2009, and the next will be on August 31, 2012. Note that blue moons, in the conventional usage, almost always fall on one of the last two days of the month, simply because in order for the phenomenon to occur, full moons must fall at the exact beginning and exact end of the month. If our standard calendar were shorter, there would be no blue moons; if it were longer, there would be many blue moons.
THE BLUE MOON IS NOT BLUE
Why "blue moons" are so named is uncertain. Certainly it is not because the moon actually appears blue the second time it rises full in a month: astronomically, there is no difference between a blue moon and any other full moon.
There are, however, such things as literally blue moons, caused by heavy smoke (for example, from forest fires) filling the atmosphere. For example, there are numerous reports of blue moons being sighted after major volcanic eruptions, such as El Chichon and Mount St. Helens; and after massive wildfires, such as the Albertan muskeg fires in 1950, which caused blue moons in eastern Canada and New England.
THE FARMER'S BLUE MOON
Early farmers' almanacs actually had a different definition of the "blue moon" than the current one, of two moons in a single calendar month. In this version, a blue moon was an extra moon during a season, not during a month. Normally, each of the four seasons of the year - spring, summer, fall, and winter - has three moons; however, every few years, there is a fourth. The farmers' almanacs identified these extra seasonal moons as blue moons.
According to a more recent article in Sky and Telescope, that magazine was responsible for introducing the popular conception of the blue moon - as the second moon in a month - in an article in the 1940s, when it accidentally misquoted a farmer's almanac.