That there are two full moons this month indicates the difficulty of trying to fit the lunar revolution period into calendars as a fixed measure of time. Moon's revolution period is incommensurate with Earth's rotation period -- that is, there are not an even number of days in the time required for Moon to orbit Earth once. In fact we even have to be quite specific in defining a complete revolution.
We can measure a complete revolution with respect to the fixed stars -- a sidereal month -- or with respect to Sun's location at the beginning of spring -- a tropical month -- or with respect to Moon's crossing Earth's orbital plane -- a nodal month -- or with respect to Moon's being closest to Earth (at perigee) -- an anomalistic month -- or with respect to Moon's position relative to Sun -- a synodic month -- and all are of different lengths.
It is the synodic month that is easiest to identify, both for us now and for ancient lunar observers when calendars were first being developed. When Moon is opposite Sun we call it full and when it is in approximately the same direction as Sun and we cannot see it we call it "new." Shortly after new moon (usually about a day later) we can see a very narrow, waxing crescent, and it was the appearance of this narrow crescent that ancient observers used to mark the beginning of a new month. The difficulty with the synodic month is that it varies from 29.26 to 29.80 days with an average length of 29.530588 days. Using it to regulate a calendar is like trying to tell time with a clock that is always running at a different rate.
The extreme variation in the synodic period is due to Moon's relatively large size compared with Earth. Moon's mass is about one eighty-second of Earth's mass, so it is very strongly affected by both Sun and Earth as the Earth-Moon system revolves around Sun. Sun exerts a force on Moon that is more than one percent of the force it exerts on Earth, and this has a significant effect on Moon's motion. Thus astronomers were not able to calculate Moon's position in orbit precisely until the beginning of this century, despite the development of Kepler's Laws and Newton's gravitational theory in the 1600's. These physical principles worked very well for the two-body problem of Sun and a planet (or a planet and a moon for planets with moons whose masses are negligible compared to the planet's), but the mathematical tools were not available for accurate treatment of the three-body problem -- Earth, Moon, and Sun -- until about 1900.
Yearly calendars that use Moon's synodic period are very complicated. The number of synodic periods of Moon and the revolution period of Earth are also incommensurate. Twelve, average synodic months make 354.3670 days while the length of our year is 365.2422 days. (Earth's revolution period and its rotation period are also incommensurate.) Use of a lunar calendar for the year required that the ancient calendar makers insert an extra month every three years. In some lunar calendars the same months have different numbers of days from year to year in order to account for variations in the length of the synodic month.
Occurrence of a Blue Moon, a second full moon in the same month, depends on the time zone where we live. Our Blue Moon is full at 11:58 p.m. EDT June 30, just barely in June. A little farther east, in, say, Halifax, Nova Scotia, full moon will occur at 12:58 a.m. Atlantic Daylight Time on July 1. Moon is full next on July 30 so that will be a Blue Moon for residents of the Atlantic time zone, but not for us in the Eastern time zone.
Even though we say "once in a Blue Moon" to indicate a rare event, Blue Moons are not extremely rare; they occur about every three years. For us in the Eastern time zone, there were Blue Moons on May 31, 1988, and August 31, 1993, and our next two will be on March 31, 1999, and November 30, 2001.