The problem of the night sky being dark
was a problem for scientists in the past. Before modern cosmology, 2 assumptions were commonly made about the universe. One, the universe is infinite in extent and second, the universe has existed forever. Olber's paradox demonstrated that at least one of these assumptions must be incorrect. An universe both infinitely old and infinitely large would result in a night sky as bright as the sun.
Modern cosmology solves the paradox in two ways. One, the universe is expanding. This means that even if the universe has been around forever, light will not be able to reach every region, even in an infinite amount of time. As well, modern cosmology suggests the universe has not existed forever, but had a beginning. Either case offers a solution to the paradox, but it just so happens both are in effect.