An "eclipse" occurs when one object gets in between you and another object, and subsequently blocks your view. From Earth, we routinely experience two kinds of eclipses: an eclipse of the moon and an eclipse of the sun.
In Chapter 26, Jacob and Bella meet for the last time in the book. Although Jacob knows his fight is lost, he pleads with her that he's the better boyfriend choice because he would've been like the sun for her, not a drug like Edward. Bella acknowledges that she's always thought of him as her "personal sun" (26.212), balancing the clouds in her life. Jacob responds: "The clouds I can handle. But I can't fight an eclipse" (26.213). Title alert!
So, apparently we're dealing with a solar eclipse here. In other words, the title seems to point to the story's resolution: Jacob, the warm sun, has been eclipsed by Edward, the cold moon. In nature, an eclipse doesn't last forever. Eventually, the sun returns, breaking through the shadow of the moon. Might that be why the sequel is called Breaking Dawn?