This theme becomes more evident near the end of the book, as Montag meets up with Granger and his people. Granger is a leader of a band of outcasts, that their society had rejected, because they wouldn't conform. Montag became one of those. He was so disgusted and disillusioned by his society that he rebelled against it, and ended up with a group of men who had a better vision for what the world should be like. As their city burns to the ground, these men could easily have left and sought refuge and cover elsewhere. Instead, they decide to go back to the city and rebuild it, because they know what mistakes had been made, and would remember not to make them again.
In the ending pages of the book, there are several quotes and symbols that Bradbury throws in to emphasize remembering the mistakes of the past. He refers to the phoenix, which is a symbolic bird that, because of its mistakes, ends up burning in a pyre of flames. But then, it "got itself born again," just to, hundreds of years later, burn himself again with the same mistakes. But, Bradbury writes, through Granger, that
"we've got one damn thing the phoenix never had. We know the damn silly thing we just did...and as long as we know that and always have it around where we can see it, someday we'll stop"
making the same mistakes. Here, Bradbury is saying that as humans, if we can remember the mistakes of the past, we can try to not repeat them again.
Granger and Montag decide that their mission is this: "remembering. That's where we'll win out in the long run." If they can just remember the mistakes that their predecessors made, then they can build a better society that won't make the same ones. And hopefully humanity will benefit as a result. History will be better if people could just remember what has done in the past, and not repeat the bad parts.
I hope that helped a bit; all of these great quotes can be found in the last few pages of the book. Good luck!