According to Noah, he and Jude "have been dividing up the world since we were five." (3.102) A shrewd businessman, when Jude wants one of his drawings, Noah takes advantage of the opportunity. "For the sun, stars, oceans, and all the trees, I'll consider it," he says. (3.102) She reluctantly agrees. "Oh, all right," she says. "I'll give you the sun." (3.107)
BOOM. Title.
So what does it mean? For one thing, these weirdly competitive twins aren't particularly good at sharing: only one of them can have the sun at once, even though, at least in theory, it's perfectly capable of shining on both of them at the same time.
Factor in the fact that Noah compares their mother, the center of their universe, to the sun in a little moment of foreshadowing ("if Mom died, the sun would go out," he says [1.147]) and you start to understand why his world has gone cold and dark.
In the aftermath of their grief, brother and sister have to find a way to reconnect and rebuild—or as Jude calls it, "remake the world." (8.256) In this new era of working together, no negotiations are necessary.