Its a common misconception that the second full moon in a month is called a "blue moon". I also made this assumption previously, however this is not the case. Having two full moons in one month does not result in a Blue Moon.
Throughout several conversations this week, I have attempted to explain why and this is the best explanation I can come up with:
The rather long background information
Our 12 month Gregorian Calendar is partially based on the 12 Lunar Cycle that often (but not always) occur in one year but individual calendars months (like August) are no longer in sync with the (approximately) 29-day lunar month (i.e. the time between two New Moons).
This results in some months (e.g those with 31 days) having two Full Moons or two New Moons.
The term "once in a Blue Moon" is not related to the number of Full Moons in one month but instead, the number of Full Moons or lunar cycles between two seasons.
Most calendars around the world have significant dates that represent the start of seasons. These dates are based on the Sun's position in the sky.
For example, in European calendars, the "Start of Spring" was usually celebrated on the 20th Mar (or 21st Mar), when the Sun is exactly level with the Earth's equator. This is referred to as Vernal Equinox where day and night are equal in length (Equi -"equal"; Nox -"night").
Likewise, the "start of summer" is usually 21st Jun or Solstice, when the Sun reaches its highest position in the sky, resulting in the longest daylight hours.
In Asian calendars, the "start of spring" (Lichun, 立春) is actually marked by the halfway point between the December Solstice and Vernal Equinox, i.e. when the Sun is 45 degrees behind (or 315 degrees in front of) its Vernal Equinox position.
The actual answer
How does the Blue Moon fit in to all of this?
Most of the time, there are three Full Moons between Equinox and Solstice (i.e. between seasons). But occasionally when a Full Moon occurs on or near the Equinox or Solstice, there will four Full Moons between the seasons. The third moon of a four moon season is called the "Blue Moon" (It will take another essay to explain why).
Consequences and Complications
Having an extra Full (Blue) Moon between seasons makes things a little bit messy, because cultural and religious festivals like Easter and Chinese New Year are based on lunar and seasonal dates.
For example, Chinese New Year is always celebrated on the New Moon closest to Lichun (the start of spring based on the Sun's position).
When there is a Blue Moon between seasons (like in 2013) it can result in the date of next Chinese New Year moving back (e.g from February to January) by almost half a month. Over several years, this gradual shift can result in Chinese New Year moving into winter months like December or November.
To accommodate this, extra/double months have to be added into the Chinese Lunar Calendar during certain years in order to push forward significant festivals, e.g. so that Chinese New Year stays close to spring/LiChun.