If there are billions of stars, why is the night sky dark?

The puzzle is old enough to have a name. If the universe were infinite, eternal, and roughly uniformly filled with stars, then every line of sight would eventually terminate on a star's surface and the entire sky would blaze as bright as the sun. It obviously does not. This is Olbers' paradox, and the resolution is not dust absorbing the light, since dust would heat up and re-radiate, but the finite age of the universe. At roughly 13.8 billion years old, light from stars beyond a certain distance has simply not had time to arrive, so we see only a finite portion regardless of how far the universe extends.

Cosmic expansion compounds it. Light from very distant sources is redshifted as space stretches, moving out of the visible spectrum into infrared and radio, so even ancient light that does arrive is often invisible to the eye. The sky is in fact glowing everywhere: the cosmic microwave background, released about 380,000 years after the Big Bang, fills the entire sky uniformly, but expansion has cooled it to microwave wavelengths just a few degrees above absolute zero. Point a radio telescope anywhere and it registers. Edgar Allan Poe, of all people, anticipated the essential answer in his 1848 prose poem Eureka, proposing that the void we see is where light has not yet had time to reach us.