A full moon is the lunar phase that occurs when the moon is totally illuminated as seen from the earth. This happens when it is on the opposite side of the Earth from the Sun; more exactly, when the ecliptic longitudes of the Sun and Moon differ by 180 degrees. This means that the hemisphere of the Moon that is facing the Earth is almost entirely illuminated by the Sun and appears round while the far side is almost completely un-illuminated.
Lunar eclipses can happen only at full moon, where the moon's orbit lets it to pass through the Earth's shadow. Lunar eclipses do not happen every month because the moon generally passes above or below the Earth's shadow which is mostly restricted to the ecliptic plane. Lunar eclipses can happen only when the full moon occurs close to the two nodes of the orbit, either the ascending or descending node. This reasons eclipses to only happen about every 6 months, and often two weeks before or after a solar eclipse at new moon at the opposite node.
The time interval between similar lunar phases the synodic month averages about 29.53 days. As a result, in those lunar calendars in which each month begins on the new moon, the full moon falls on either the 14th or 15th of the lunar month. Since calendar months have a whole number of days, lunar months may be either 29 or 30 days long.