Epigraphs are like little appetizers to the great entrée of a story. They illuminate important aspects of the story, and they get us headed in the right direction.
"It is good to renew one's wonder," said the philosopher. "Space travel has again made children of us all."
As far as we can tell, this isn't a real quote; it's just something Bradbury thought up and liked.
So what does it mean? The part about "wonder" reminds us not to take things for granted. "Wonder" can refer to curiosity ("I wonder what Mars is like") but also something like amazement ("Wow, this new bath cleaner is wonderful"). In this context, it probably means something more along the lines of amazement, like a child discovering the world for the very first time.
One way to avoid taking things for granted is to go look at new things. After all, that's why babies and children are so often surprised—to them, everything is new. That helps explain the last part of the epigraph: Space travel allows us to go out and see new things. We may be senile old fogies in relation to Earth, but in relation to Mars we're just babies.
Finally, note that Bradbury has a "philosopher" say this. If you're someone who likes business and industry, philosophy may seem frivolous. By having a philosopher introduce his stories, Bradbury is telling us to listen to those guys. After all, these aren't meant to be stories about how amazing and successful the Mars mining operations were—they're more about how all the philosophers were right, and all the greedy technocrats were wrong.