In simplistic terms, Marvin and his father leave the colony to see Earth. In plot terms, this is a coming-of-age story, and the trip to see the Earth is a sort of "rite of passage" for Marvin, bringing him closer to adulthood.
The trip is clearly of importance to the boy, because in the first paragraph he states that he has never been beyond the Observatory, and giving it the capitalized, proper-noun name "Outside" suggests both his stated excitement and the importance that this place holds. It quickly becomes clear that Marvin hasn't even seen the sky, or the real surface of the place that he lives (which we might guess to be the Moon, but it isn't explicitly stated at this point in the text).
Much of the text is concerned with Marvin's sense of wonder at all the things he hasn't seen before, and how beautiful yet desolate these things seem to be. When he finally sees Earth, he is predominately concerned with its beauty and apparently peaceful and benevolent appearance; it is only upon closer inspection that he sees and recognizes the signs of nuclear war. In this moment, Marvin undergoes a subtle transformation; the "fairy tales" that he had been told about Earth, and its destruction, suddenly gain substance.
That was the dream: and one day, Marvin knew with a sudden flash of insight, he would pass it on to his own son,
Marvin essentially "grows up" at this moment, experiencing what in literary terms is called a loss of innocence, and he begins to realize his place among the colonists not merely as a child, but as an inheritor of the human legacy.