The dark and bright side of anything is related to light exposure
the bright half of the moon indicates the exposure of half of the moon is towards shining sun rays. The dark half of the moon is due to non exposure of that half part to shining sun rays. As moon revolves around sun the shape and side of this shining and dark moon changes with time.
Moon completes its one turn in around 27 days.
Due to movement of moon with respect to sun also we observe darkness and brightness on different parts of moon during one complete cycle.
