Every month as the Moon cycles through its phases it appears to change shape. The Moon always has the same spherical shape, but stargazers on Earth see different fractions of the dark and illuminated portions of the Moon as the Moon orbits Earth. The common urban myth that Earth's shadow falling on the Moon causes lunar phases is incorrect.
Phases of the Moon
The Moon starts its cycle of phases with the new Moon. As the Moon orbits Earth, a few days after the new Moon a waxing crescent Moon is visible in the western sky just after sunset. Each night the crescent Moon is a little larger and higher in the sky.
About a week after the new Moon, the Moon appears as a half circle. This is the first quarter Moon. Many people call this phase the half Moon, but half Moon is not the correct astronomical terminology.
As the Moon continues to wax, it appears as more than a half but less than a full circle. This phase is the waxing gibbous Moon.
About two weeks after the new Moon, stargazers on Earth see the full Moon. The full Moon appears as a full circle in the sky. then the waning lunar phases begin.
As the Moon wanes, it goes through the waning gibbous phase. Then earthbound stargazers see the third quarter Moon about a week after the full Moon. As the Moon continues to wane, it goes through the waning crescent phase. The waning crescent gradually gets smaller and closer to the Sun in the predawn sky. About 29.5 days after the previous new Moon, the Moon is again new. The lunar cycle repeats.
Cause of Moon's Phases
At any given time, half of the Moon is illuminated by the Sun and the other half is dark. The lunar phase seen from Earth depends on what fraction of the illuminated and dark portion of the Moon is visible from Earth.
During the new Moon phase, the Moon is between the Sun and Earth. The dark portion of the Moon faces Earth, so the Moon is not visible during new Moon. Usually the Moon is either north or south of the Sun, but occasionally the Moon lines up directly between the Earth and Sun. Then Earth has a solar eclipse, which can only occur during the new Moon.
As the Moon continues its monthly journey around Earth, a small portion of the illuminated side of the Moon begins to face Earth. Earthbound stargazers see a waxing crescent Moon low in the west just after dark.
The Moon's orbit continues. When the Moon is one quarter of the way around its orbit, it is 90 degrees from the Sun as seen from Earth. Half of the side of the Moon facing Earth is illuminated by the Sun. The other half is dark. Observers on Earth see the first quarter Moon. A few days later, observers see a waxing gibbous Moon because more than half of the side of the Moon facing Earth is illuminated by the Sun.
When the Moon is directly opposite the Sun in the sky, observers on Earth see only the illuminated portion of the Moon. The Moon is full. If the Moon lines up so that Earth is directly between the Sun and Moon, then Earth's shadow can fall on the Moon causing a lunar eclipse.
As the Moon continues orbiting Earth, it goes through the waning gibbous, third quarter, and waning crescent phases. The waning phases are similar to the corresponding waxing phases, but because they are on the opposite side of the Earth, observers see the opposite side of the Moon illuminated.
As the Moon orbits Earth every month, it cycles through the lunar phases because different fractions of the dark and illuminated portions of the Moon face Earth.