I have smart readers! 60% of you who responded to the poll got the right answer: scattering. And nobody took the dunce's answer (pigment).
The simplified explanation: if the atmosphere above us was perfectly transparent (so that the sun's light shined straight through it), the sky would be pitch black. But a phenomenon called “Rayleigh scattering” causes a little of the sun's light to be scattered in random directions, which is why the sky isn't pitch black. Rayleigh scattering is sensitive to the light's wavelengths – shorter wavelengths (the blue end of the spectrum) are scattered more than longer wavelengths.
And that, my friends, is why the sky is blue and not black. Much more, including the interesting effects of Mies scattering, here, here, here, and here.
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