The moon does reflect light from the sun, which is why it is visible in the night sky. The actual surface of the moon is mostly a dark grey color, reported by astronauts who have walked on it, but it appears a bright yellow or white in the sky due to the reflected light.
The moon reflects a different amount of light depending on where it is in Earth's orbit. When the moon is directly between the sun and Earth, humans are unable to see it as no light is directed towards the planet's surface. As it moves around Earth, more and more of the light is reflected until humans see a full moon.