What was the author's purpose for writing Guns, Germs, and Steel?

Diamond's purpose in writing this book was to answer
"Yali's Question."  This was a question which had intrigued him for some time and he
wanted to use his scientific background to help find an
answer.

Yali's question centered around human history. 
Yali wanted to know, essentially, why white people have so much wealth and power in the
world when compared to the people of most non-white countries.  He wanted to know why
Europeans were able to dominate the world.

Diamond's
purpose in writing the book, then, is to put forward his answer to this question.  His
answer is based on geography rather than on race or culture.  He argues that
geographical luck is what made Europe come to dominate the
world.