Final answer:
When less than half of the side of the Moon facing Earth is in sunlight, it is called a crescent moon. This crescent moon can be faintly outlined by earthshine, which is light reflected off the Earth. The quarter phases of the Moon provide the best views of its surface topography.
Step-by-step explanation:
When less than half of the side of the moon facing Earth is in sunlight, we see a moon phase called a crescent moon. This is part of the lunar cycle where the Moon appears to shrink or grow, depending on its position relative to the Earth and Sun.
During the new moon phase, the side of the Moon that is illuminated by the Sun is not visible from Earth and the Moon rises and sets with the Sun. However, interestingly, when only a narrow crescent of the Moon is visible, a phenomenon known as earthshine can occur, allowing us to faintly see the rest of the Moon's surface due to light reflected off the Earth's surface.
When observing the Moon's surface with binoculars or telescopes, the details of the surface are most dramatic when the Moon is at a quarter phase, due to the oblique lighting casting sharp shadows on the Moon's topography, enhancing its features.