Every month as the Moon cycles through its phases it appears to change its shape. The Moon of course always has the same spherical shape. There is a common urban myth that Earth's shadow falling on the Moon causes lunar phases. As logical as it seems, this myth is incorrect.
A few simple observations of the Moon's position in the sky relative to the Sun demonstrate that Earth's shadow can not cause the lunar phases.
Full Moon
Observe the full Moon's location in the sky. The full Moon rises in the east as the Sun sets in the west. It also sets in the west as the Sun rises in the east. As seen from Earth, the full Moon is directly opposite from the Sun in the sky during the full Moon.
When Earth's shadow falls on the Moon, however, Earth is between the Sun and Moon so that the Moon is directly opposite the Sun in the sky, as seen from Earth. If the Earth's shadow falling on the Moon caused the lunar phases, then when the Moon was directly opposite the Sun in the sky, it would be a dark new moon or very thin crescent rather than a bright full Moon.
Observations of the full Moon's position in the sky are not consistent with the idea that Earth's shadow causes phases of the Moon.
Crescent Moon
Observing a crescent Moon also shows that Earth's shadow can not cause lunar phases. If Earth's shadow causes lunar phases, then the crescent Moon should be in Earth's shadow because most of the Moon is dark during the crescent phase. Can the crescent Moon be in Earth's shadow?
The waxing crescent moon, just after the new Moon, is visible low in the western sky just after sunset. The waning crescent Moon, just before the new Moon, is visible low in the eastern sky just before sunrise. As seen from Earth, the crescent Moon is always fairly close to the Sun's position in the sky. With this configuration, it is impossible for Earth's shadow to fall on the Moon.
If Earth's shadow caused the lunar phases, the crescent Moon would have to be mostly in Earth's shadow. Hence the crescent Moon would have to be nearly opposite the Sun in the sky. Observing the crescent Moon's position in the sky relative to the Sun shows that the crescent Moon can not be caused by Earth's shadow falling on the Moon.
Analyzing simple observations of the Moon's position in the sky during lunar phases shows that Earth's shadow can not cause phases of the Moon.
The Moon's phases instead result from the relative positions of the Earth, Sun, and Moon and from the fractions of the night and day side of the Moon visible from Earth.