Now that she isn't going to be executed for murder (whew!), Daphne leads Mau back to the Grandfather's cave to show him what she saw: a globe.
It's upside down (at least by our standards), but it's an accurate representation of the world. In an ancient cave. That's been untouched for centuries.
Daphne says, "I think people from this island sailed around the world, a long, long time ago. You remembered, but over the years it became a story for little children" (12.49).
Mau is in awe that his ancestors were such worldly, knowledgeable people. In fact, they might just be the oldest people on Earth, the origin of humanity.
They also find false gold teeth down there, which makes Mrs. Gurgle happy.
Pilu tells the story of this new finding to the people, with just a few embellishments.
Now that they've dual-handedly changed human history (that was easy!), Mau and Daphne are worried that something Foxlip said about Mr. Cox may have been true: that Cox is leading the cannibalistic Raiders now.
To prepare for invasion, Mau runs the people through a series of drills. They're about as successful as Duck and Cover would have been, but A for effort.
Daphne tries to help Mau with his people-managing skills, but she has genuine doubts that they'll be able to survive.