It’s not actually black like a piece of coal, it’s black because most places that you look in the night sky don’t have a sufficiently bright star in them, so you just get the absence of light.
The fact that the night sky is dark was actually pointed out to be odd if the Universe goes on forever and has stars spaced out more or less evenly throughout, it’s called “Olbers’ paradox”: http://en.wikipedia.org/wiki/Olbers'_paradox
These days we don’t think that the universe goes on for ever (it started with the Big Bang and is still expanding), so the paradox isn’t a problem any more!
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We see the sky as different colours on Earth, as all the tiny particles in the atmosphere scatter the light from our Sun in an effect we call “Rayleigh scattering” – the shortest wavelengths of sunlight (the blues and purples) are scattered better than the longer ones (the reds and oranges) and hit our eyes, so that’s the colour we mainly see.
So the sky appears black at night because, as Grant says, there is simply no sunlight hitting the Earths’ atmosphere for any of the colours to be scattered into our eyes. This is why in all the pictures of the Apollo astronauts on the Moon, the sky is black all of the time – because the Moon has no atmosphere, no sunlight can be scattered. 🙂
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