The main problem that Diamond is addressing in this book is "Yali's Question." It is the issue of why European societies have come to dominate the world.
Yali was a native of New Guinea who asked Diamond why it was that white people had so much wealth compared to the natives in New Guinea. Diamond expands that question in this book to ask why European societies have become dominant in so many (economic, political, technological, etc) ways.
In order to answer this question, Diamond then turns to a huge variety of evidence. Most importantly, he looks at geographic factors such as the presence of plants and animals that could be domesticated and the length of the "axes" of the various continents. Diamond uses these geographical factors to try to account for the fact that European societies have come to dominate the world.