What is the big question that Professor Diamond wants to answer in Guns, Germs, and Steel?

The big question that Jared Diamond is trying to answer in Guns, Germs, and Steel comes from what is called “Yali’s Question" in the book.  It is found on p. 14, in the Prologue.  There, Yali (a native of New Guinea) asked Diamond

Why is it that you white people developed so much cargo and brought it to New Guinea, but we black people had little cargo of our own?

When Yali talks about “cargo,” he means wealth and technology.  In essence, he is asking why “white people” became rich and powerful and “black people” did not. 

That question stuck with Diamond and he eventually wrote Guns, Germs, and Steel to answer it.  By the time he came to write the book, the question had expanded somewhat.  On p. 16, Diamond gives a rephrased version of Yali’s question.  There, he says that he is trying to find an answer to the following question:

why did human development proceed at such different rates on different continents?

In Guns, Germs, and Steel, then, Diamond is trying to account for one of the fundamental facts of world history.  He is trying to answer the big question of why Europeans and their descendants have come to (at least for the past couple of centuries) dominate the world.