According to Guns, Germs, and Steel why do the histories of the Fertile Crescent and China hold important lessons for the modern world?
The answer to this can be found in the Epilogue. Specifically, it can be found on page 417 of the paperback edition of the book. On that page, Diamond says that
The histories of the Fertile Crescent and China also hold a salutary lesson for the modern world: circumstances change, and past primacy is no guarantee of future primacy.
Let us think about what he means by this.
In this chapter, one thing that Diamond points out is that China and the Fertile Crescent each held huge technological leads over Western Europe at various points in history. However, those regions were unable to hold their leads. The Fertile Crescent lost out because the land was too ecologically fragile to continue to support large populations. China lost out because it was too connected and therefore too able to dominate its region. It had no rivals in its region and did not have to compete.
The lesson, then, is that we should not think that societies that are ahead in the world can never lose their lead. Instead, we have to realize that things can change. New challenges can arise that make an area that was once dominant become very weak. This is the lesson that Diamond wants us to learn from the histories of these areas that once were dominant.