The best place to find a brief version of this answer is on p. 370 in my copy of the book.
According to Diamond, there are three sets of what he calls "ultimate factors" that are responsible for allowing the Eurasians to defeat the Americans. These are:
- Eurasia had people long before the Americas had people. So the Old World had a huge head start on building civilizations.
- Eurasia, for geographical reasons and because of luck, had better food production.
- Eurasia, for geographical reasons (mainly the long east-west axis) was more conducive to having innovations spread across it. Thus an innovation discovered in one place could spread across the whole area.
Diamond says that there is one more cause that is "more speculative." He thinks that it is the fact that the Americas' population centers were widely separated and had few connections with each other.