Moon phases
Why does the Moon change shape?
The Moon makes no light of its own. One half is always lit by the Sun. Phases are your changing view of that lit half as the Moon goes around Earth — about 29.5 days from full moon to full moon.
Nothing happens to the Moon
Between Earth and the Sun, the lit side faces away from you: new moon. On the opposite side of us from the Sun, the lit side faces you square on: full moon. Crescents and gibbous shapes are everything between.
The dark part is not Earth’s shadow. Earth’s shadow is a narrow cone, and the Moon misses it most months. The dark part is simply night on the Moon.
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A month is this cycle
Full moon to full moon is a synodic month, about 29.5 days — longer than one trip around Earth relative to the stars (the sidereal month, about 27.3 days), because Earth has moved along its own orbit and the Moon has to catch up to the same Sun angle.