The length of the month is determined by the regular variation in the appearance of the Moon, i.e., by the changing phases of the Moon. The changing of the phases of the Moon defines the Synodic Month. The different phases of the Moon are due to changes in the relative orientation of the Earth, the Moon, and the Sun. The changing of the phases is due to the orbital motion of the Moon about the Earth.
The Moon orbits around the Earth in the CCW-sense as viewed from the
North, the orbital plane is inclined at angle of 
5 degress with
respect to the ecliptic plane (i.e., it is nearly co-planar with the
orbit of the Earth), and the
orbital period of the Moon about the Earth
(the sidereal revolution period which defines the sidereal month)
is 
27.3 days.
The synodic period (the period of the lunar
phases)
is 
29.5 days.
Note -- The solar day (based on the Sun crossing the meridian two succesive times) is longer than the true day, the sidereal day. It turns out that the month based on the phases of the Moon (the synodic month) is also longer than the true month, the sidereal month.
Why is this true? Hmmm
Hmmm, a given rises earlier from night to night (by 4 minutes). Does the Moon rise later or earlier from night to night? (By how much?)
