The moon appears black at night in regions where it isn't illuminated by the sun because it doesn't produce its own light; it only reflects the sunlight that reaches it. The part of the moon that looks black is actually just in shadow, either because the sun's light is hitting the other side of the moon or because the Earth is blocking the sun's light from reaching the moon during certain phases, such as during a new moon.
During a new moon, the side of the moon facing Earth is in complete shadow, making it appear dark or virtually invisible to us. When you can see only part of the moon illuminated, and the rest appears dark, this is due to the varying angles from which sunlight strikes the moon's surface as it orbits around the Earth.