A simple paradox, and an old one
Picture an infinite, eternal universe with stars more or less everywhere. Aim your eyes in any direction at all, and if you keep going far enough you have to land on a star eventually: the further you look, the more of them there are. The sky should therefore be lit everywhere, as bright at midnight as it is at noon.
That is plainly not what we see. Between the visible stars, the night is dark. The German astronomer Heinrich Wilhelm Olbers stated the paradox in 1823, though Kepler had already puzzled over it two centuries earlier. The fact that night is dark is itself a major piece of cosmological information: the universe, as we naively imagine it, cannot be what we think it is.
The universe has an age
First answer: light is fast, but not instantaneous. It travels at 300,000 km/s, quick, yet finite. And the universe is not eternal. It began about 13.8 billion years ago. The light from a star 100 billion light-years away has therefore never had time to arrive. It is still on its way.
When we look up, we only see the objects whose light has had time to cross the distance. Past a certain radius (what cosmologists call the cosmological horizon) there may well be myriads of stars, but their light hasn’t reached us yet. They don’t exist for us, not yet. And that single fact is enough to open up vast genuinely empty stretches of sky.
The poet Edgar Allan Poe, oddly enough, glimpsed this answer in 1848 in his essay Eureka, before science had formally proven it. He pictured “the distance of the invisible background so immense that no ray from it has yet been able to reach us at all”.
And it’s stretching
Second answer, more subtle: the universe is expanding. Since the Big Bang the galaxies have been moving apart, and the further away they are, the faster they recede. That stretching doesn’t only carry them along. It also tugs on the light itself. Light waves crossing a space that is growing get longer. Their frequency drops, their colour shifts toward red, then into the infrared, and, for the most distant galaxies, out of the visible spectrum entirely.
What ought to reach us as visible light arrives instead as microwaves. If our eyes were tuned to that wavelength, the sky wouldn’t be dark: it would glow uniformly in every direction. That glow exists, and our radio telescopes pick it up. It’s the cosmic microwave background, and it corresponds to the light emitted about 380,000 years after the Big Bang, stretched along the whole journey.
In other words: the sky is bright. We just don’t see it, because the brightness has been reddened so far that it falls outside our eyes. The darkness you see when you look up at night is the skin of the universe — retraced at the limits of our own vision.