The daily rising and setting of the Sun, the year of the Sun's seasons, and the monthly period for the phases of the Moon were important cyclic events for ancient peoples. All these repetitive cycles were important to them in establishing both a concept of time and a means of marking its passage.
Our understanding of the reasons for the Moon's phases predates even Aristotle, who was aware that the Moon "shines" by reflecting sunlight. The parallel rays of the distant Sun always illuminate one-half the Moon's surface as well as one hemisphere of the Earth; when the Moon is visible, we are seeing rays of sunlight reflected off the Moon's surface.
When the Moon is between the Earth and the Sun--the time of a new moon--its dark side faces us, and we do not see it at all. Because the Moon moves eastward relative to both the Sun and stars, within a few days a thin crescent appears low in the western sky after sunset and sets shortly after the Sun. In the next few days, a growing crescent appears higher in the sky after sunset and therefore sets later on successive nights. One week after new moon, the Moon is at first quarter and will be on the celestial meridian at sunset; it will set about 6h after the Sun. In the following week, the Moon, now more than half a crescent, becomes full as it continues its easterly movement around the Earth. Two weeks after new moon is the time of full moon, when the Moon lies on the opposite side of the Earth from the Sun. We see it rise at approximately 6 P.M. and set about 6 A.M. One week later the Moon is at last quarter where it rises about midnight and sets around noon. Finally, we see the declining crescent-shaped Moon rise shortly before sunup as it is about to overtake the Sun one month after the previous new moon.
If we observe the Moon's movement against the stars, we find that it moves a little over a 0.5o per hour, or about 13o per day. Thus the Moon takes around 27.3 days to complete its orbit of 360o; this period is called the sidereal month. However, because the Earth is also moving around the Sun, the time between two successive cycles of lunar phases is longer than the sidereal month. Although the Moon has completed its revolution around the Earth at the end of 27.3 days, it takes about 2 more days to bring the Moon back to the Earth-Sun line so that it again appears as a new moon. Thus the period of lunar phases, the synodic month, is 29.5 days.