I know that the the visible moon is due to sunlight reflecting off it, back to us. However, how can the moon be so bright yet the surrounding night sky be so dark?
maybe it's bright, not bright as moon itself,
think there's no object to reflect moon's reflection or sunlight. and even if there are small object, reflection would be so small, so it won't reach before our eyes, or camera lens. this is all I can think about.
Well quite. Why should it be bright? There is not a lot in space to reflect light back to you. The moon is not bright enough to cause the refractive scattering that makes the sky appear bright during daytime, so the background must be dark. Darkness is only the absence of light, after all.