This question had been asked by scientists for so many years without an acceptable answer that it became known as Olbers’s Paradox. Until very recently, scientists theorized that spaced stretched on in all directions, forever, and that there were an infinite number of stars in it. If this were true then there should be a star everywhere that we look and the night sky should be blindingly bright.
In the 19th century, an astronomer named Wilhelm Olbers suggested that the reason this was not true was due to space dust. He thought that perhaps the reason we could not see light from very distant stars was because the dust in space absorbed it. After Olbers’s death, scientists determined that the starlight from all of the suns out in space should heat up the space dust sufficiently so that it glowed too. That is how this question, "Why is space black?" was called Olbers’s Paradox.
Edward Harrison, an astronomer at the University of Amherst in Massachusetts has recently written a book called Darkness at Night: A Riddle of the Universe. In it he states that the night sky isn’t blindingly bright because the stars and the universe don’t actually go on forever. Light can take millions of years to reach us from the stars that emitted it. Therefore, when we look out into space we are actually looking back in time. Powerful telescopes now allow astronomers to see light that was emitted by stars approximately 10 billion years ago. As telescopes become more sensitive, scientists are able to look further back into time. Many scientists believe that the universe is only about 15 billion years old.