On Earth, you witness moon at two possible times:
- It's night, and not a new moon.
- Sun is on the horizon, about to set in your part of the world.
During both the times, sunlight does not have the intensity as during the day and thus, the moon is visible. And I guess it's safe to say everyone knows why it appears bright. Because sunlight bounces off of it and is incident on the Earth's surface.
In Space, there is no such thing as atmosphere. As a consequence, sunlight radiates in all the directions equally. The moon doesn't still look completely dark even in space. It has a certain brightness coefficient associated with it, but it is certainly lesser than what it is as seen from Earth.

As you can see, moon is not completely dark, as seen from space. It is still shining from the little amount of light reflecting off its surface.
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