A phase of the moon that occurs when the moon lies on the opposite side of Earth from the Sun. The moon as seen from the surface of the Earth is fully illuminated by the Sun at this time, presenting a "full" round disc to Earthly viewers. Note that, as is always the case during any phase, only half of the total surface of the moon is illuminated.
A full moon is the only time when a lunar eclipse is possible: at that time the Moon may move through the shadow cast by the Earth. However, because of the tilt of the moon's orbit around the Earth relative to the Earth's orbit around the Sun, the Moon may pass over or below the shadow, so a lunar eclipse does not occur at every full moon. Full moons are otherwise a poor time to conduct astronomical observation, since the bright reflected sunlight from the moon overwhelms dimmer phenomena.
An approximate formula for the average time of full moon N is:
D = 20.362954 + 29.5305888531*N + 102.19E-12*N*N,
where D is the number of days (and fractions) since 1 January 2000 00:00:00 TT, and N is an integer.
To obtain this moment expressed in universal time (world clock time) for future events (N>0), apply the following approximate correction:
-0.000739 -235E-12*N*N days
The true full moon may differ from this by over 14 hours due to periodic perturbations. The long-term error of the formula is approximately: 1*cy*cy seconds in TT, and 11*cy*cy seconds in UT (cy is centuries since 2000); /details.
The Blue Moon
The event known as a blue moon is related to the western calendar system. A blue moon is when two full moons occur in the same calendar month. Blue moons occur infrequently (thus the saying once in a blue moon to denote a rare event) because the length of the calendar month in this system is near to the length of the period of the Moon's phases (synodic month). They are not impossible since every month except February is longer that this period by 1 or 2 days.
The original meaning of blue moon was the third full moon in a season when there were four full moons in that season: this had to do with church Holy days related to the last or first full moon of a season (like Easter). This usage had been almost entirely forgotten, and the original meaning was uncovered only when researchers for Sky & Telescope Magazine noticed that the Maine Farmer's Alamanac from 1829 to 1937 reported blue moons that did not fit the first meaning of the term as listed above. (See http://www.skypub.com/sights/moonplanets/9905bluemoon.html).