This is a fantastic question—and the answer is deceivingly complicated! You might assume that, in an infinite and unchanging universe, no matter which direction you look at in the sky, you would see a star at some distance. Since many stars out there are just as bright as or even brighter than the Sun, the night sky should be filled with light and thus always look like day. However, we have made some incorrect assumptions. We now know that the universe is not static nor infinite! We know that at some point near the beginning of time, there was the Big Bang, and that over the course of the universe’s lifetime stars are formed and die away. We also know that space seems to be expanding within our universe. Using these clues, we can piece together why the night sky is dark:

First, because there are a finite number of stars, there will be points in the night sky where there is no light coming from a star. In addition, because light takes time to travel to us, what light we are actually seeing is from a long time ago—and much of that light could be millions or billions of years old when many stars in the sky have not been formed yet! Many (billions) years into the future, our night sky may be brighter because more light from newer stars will have had time to reach us.

Secondly, we know there are other celestial objects that absorb light. Just as the Earth absorbs the light hitting us, other planets, gas clouds, black holes, or even stars will absorb light and thus prevent us from ever seeing it. Lastly, we know that the universe is expanding, which means all the stars are moving away from us. There is a phenomenon call red-shifting which means light being emitted from a moving body has its color (or wavelength) shifted. The stars are moving so fast away from us that visible light is red-shifted into the infrared spectrum, which we cannot see with our own eyes!

Hence, these reasons are why the night sky appears dark to us, but may not be all that dark! The Wikipedia article on the night sky paradox: click here

A really nice summary YouTube video made by MinutePhysics: click here to watch video

As scientists, one of the things that we do is make observations and try to form a good guess of how the world works based on our observations. You made a good observation when noticing that, despite billions and billions of bright stars in the sky, sometimes you don’t see any at all!

Let’s make some more observations. Our own star, the Sun, is really, really bright. Sometimes though, like when grey clouds cover the sky in Santa Barbara, we don’t see the sun at all. It’s not that the sun isn’t there. The clouds in the sky just cover it up! The same thing could happen at night.

But what about on a perfect, cloudless night? I visited Los Angeles, and there were almost no stars even on a clear night. Well, that might be due to light pollution. Street lights, lamps shining through office windows, headlights, and others can all contribute to light pollution. The bright, glowing artificial light that we create makes it so we can’t see the stars in the sky. If you stood in the middle of downtown Los Angeles at night, you probably wouldn’t see much. But if you drove a couple hours towards the mountains, it would look like more and more stars came out when really, there’s just less light blocking them!

The sun is really, really bright though, and other stars are probably really bright, too. If there are really billions and billions of stars, how come it only looks like there are maybe a few thousand in a clear night sky with no light pollution? Well, astronomers measure how bright stars are in “apparent magnitude” and “absolute magnitude”. Apparent magnitude is how bright a star looks from Earth; it’s apparently this bright. Absolute magnitude is where we say, if all stars were the same distance away, how bright would they be? A shimmering star brighter than another but a lot farther from Earth might be brighter if both stars were the same distance away (higher absolute magnitude) but would look dimmer from Earth (lower apparent magnitude).

Some stars are so far away that you can’t see them unless you have a telescope. Some stars are even further away in different galaxies, and even the most powerful telescopes can barely see that galaxy! Fun fact: the brightest star that we know of is 8.7 million times brighter than the sun, but this star is so far away that it would be hard to see without a telescope! So, to see stars in the sky, you need a clear night, no light pollution, and a bright star that’s close enough to Earth.