Short answer: The Moon changes its apparent shape because we see different portions of its sunlit side as the Moon orbits Earth. The phase cycle is caused by the geometry of Sun–Moon–Earth: from our vantage point we see varying fractions of the lit half of the Moon, so it appears to wax and wane over about a month. Details

• What governs the changes
  • The Moon stays roughly the same size and shape in reality; what changes is how much of its illuminated side is visible from Earth as the Moon travels around our planet. This is a result of the relative positions of the Sun, Moon, and Earth during its roughly 27-day orbit and a bit more for the full cycle that includes the Moon’s orbital tilt and the Sun’s light direction.

• The common phases
  • New Moon: the Moon lies between Earth and the Sun; the illuminated face is away from us and generally not visible.

* Waxing crescent to first quarter: a growing sliver becomes visible as the Moon moves in its orbit.

* Waxing gibbous to Full Moon: more of the lit side becomes visible, culminating in a fully illuminated disk at full Moon.

* Waning phases: after full Moon, the visible illuminated portion decreases through waning gibbous, third (last) quarter, and waning crescent back to new Moon.

• The “why” behind the same-face view
  • The Moon is tidally locked to Earth, rotating once per orbit so the same hemisphere faces Earth at all times. This is why we never see the far side from Earth, and why the cycle is about what portion of the near side is lit and visible.

• Quick physics intuition
  • The Sun lights up half the Moon at any moment, but our viewpoint changes as the Moon orbits. The changing angle between Sun, Moon, and Earth determines which part of the lit face is visible, creating the familiar sequence from new to full and back.

If you’d like, I can tailor a simple explanation for kids, a quick diagrams guide, or point you to a reliable, up-to-date visualization of the Moon’s phases.