The moon shines as a result of the reflection of the light from the sun. The rocky surface of the moon reflects light from the moon and as a result of its closeness to the earth, it appears to shine.
1 Additional Answer
The moons light is provided by light reflecting off the sun. The surface of the moon i quite rocky and does not provide that much light. The moon is close enough to the earth to provide light at night when half to full moon. You can find more information here: http://planetariumweb.madison.k12.wi.us/mooncal/moonfaq#8