The Martian Chronicles is a very fragmentary book. Many of its stories were written to stand alone. Therefore, any analysis of the book should first state what the novel manages to achieve as a whole. Obviously, it is a fictional account of the colonization of Mars. NASA repeatedly sends teams to explore; finally, one of them is successful. What follows is rampant settlement, much like Westward Expansion in American History. Some are looking for escape from civilization, but most only want to bring civilization to Mars--American civilization, that is. Finally, atomic war breaks out on Earth, and so all the humans go home. A few humans flee the war and head to Mars; when they get there, they don't make the mistake of trying to recreate American civilization. They have seen that the result of Earth civilization was war, so they burn their maps of Earth and decide to become Martians. Bradbury's message is that some types of colonization are right and others are wrong. Trying to replicate the old civilization is wrong, but appreciating the civilization you have found is right.
Beside this warning against reckless exploration and expansion, Bradbury is also simply writing a story about the American Dream of the frontier. He writes exciting tales about the dangers the first explorers face, and one is reminded of cowboys and Indians. He writes about the loneliness of the frontier, about how different people approach the idea of a new landscape. He shows how the American Dream can lead to misunderstandings and waste, and he shows the diversity of that dream, in disaffected literati like Stendahl, in oppressed Negroes like Silly, in rowdy young men like Sam Parkhill.
There are no major characters in The Martian Chronicles, and its plot, as stated above, does not move steadily from story to story. Why, then, is the novel so famous? First, it was a function of the novel's crossover appeal--it was a science-fiction novel that non-sci-fi fans could enjoy. Second, it is a very poetic novel. Whether you think the "poetry" is good or bad, it cannot be denied that, for a novel about outer space, Bradbury pays an extraordinary amount of attention to physical beauty, to familial ties, and to eerie, chilling atmospheres.