| As Hubble discovered, the further away you look, the more redshift you see. This (combined with the spectrum of stars, which is really just a consequence of what black body radiation, or Planck radiation, looks like), resolves Olbers' paradox (Go read that node, if you haven't yet, or nothing makes sense).
Now, when you're looking at a very distant star, its light is redshifted. But the star radiates less at higher frequencies, and radiates nothing beyond a certain frequency. Combining these two facts gives you that you see a lot less radiation from distant stars; their light drops off by more than just the inverse square law effect of their distance. So looking at a point in the dark night sky (or the daylight sky, for that matter), you might be looking at an extremely distant light source, but it's so redshifted that the portion of its spectrum that is redshifted into what you see is negligible. And most of its energy output is transformed into very low frequencies, effectively vanishing.
Once again, physics ends up saving the day. Well, not really. All this lengthy explanation of Olbers' paradox ends up saying is that some lengthy line of reasoning, which would have wiped everything out if true, is fallacious. So none of this happens, and the night sky is appropriately dark, not lit up like the sun.
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