Why does the Moon cycle from New Moon to Full Moon?

Answer 1

The Phases of the Moon are caused by the amount of lighted Moon surface that is visible from Earth. That changes in standard cycles of 29.5 days as the Moon circles the Earth and the Earth circles the Sun.

Half of the Moon is always lit by the Sun, the same as all the planets and satellites. At different times of the month, different amounts of that lighted surface are visible from Earth. If the Moon is between the Sun and Earth, we see only the dark side. If the Moon has circled to the other side of the Earth, away from the sun, we see the lit side.

For instance, at the time of the Crescent Moon, the whole Moon is there, but we are seeing (or not seeing) mostly the unlit side of the Moon. At that time, because of the positions of the Earth, Sun and Moon, only the edge of the lit part is visible from Earth.

Answer 2

The Moon cycles from New Moon to Full Moon due to its position relative to the Earth and the Sun. During a New Moon, the Moon is positioned between the Earth and the Sun, with the side illuminated by the Sun facing away from us. As it orbits the Earth, we progressively see more of the illuminated side until it reaches the Full Moon phase, where it is directly opposite the Sun from our perspective.