The story is set on a lunar colony after a nuclear Armageddon on earth. The simple point of the story is a warning of impending doom if the world doesn't get a handle on the proliferation of nuclear weapons. When the story was written in the 1950s, the threat of atomic weapons was much more on the forefront.
However, the point of the story also serves a deeper meaning concerning protecting what we have on earth now. In the story, Father is showing his son the former glory of earth as a motivation for the future and a warning. If we, as parents, fail to protect what we have, whether it be the earth, our culture or family traditions, then our children won't have the same understanding of the world. This is demonstrated by Marvin's inability to understand the nursery rhythm "Twinkle Little Star". To him the stars always shine bright and full because the moon has no atmosphere and he has never experienced life any other way.
The final message to parents is to introduce our children to the greater glory of our past and encourage them even when all seems lost. There is a need to work for something beyond what we can achieve. Sometimes it is better to show our children than to just tell them.