In Guns, Germs, and Steel, Diamond uses the Spanish conquest of the Incas to illustrate what he calls the proximate causes of European domination. He lists a number of factors that allowed the Spanish to conquer the Incas rather than the other way around. He uses the capture of Atahuallpa as a story in which we can see these various factors playing out. You can find these factors summarized in one sentence at the bottom of page 80. There, Diamond tells us that
Immediate reasons for Pizarro's success included military technology based on guns, steel weapons, and horses; infectious diseases endemic in Eurasia; European maritime technology; the centralized political organization of European states; and writing.
These are the factors that, in Diamond’s view, allowed the Spanish to conquer the Incas rather than the Incas being able to go across the Atlantic to Spain and conquer that country. Diamond boils these many factors down into three factors. These three factors are the “guns, germs, and steel” that make up the title of the book.
However, Diamond does not think that it is all that important to know these proximate causes of the Spanish conquest. These causes are, after all, fairly obvious. Instead, Diamond thinks that it is much more important to understand why the Spanish came to have all these advantages. Why, in other words, did the Spanish (and not the Incas), have the “guns, germs, and steel”? That is the real question that Diamond will answer in this book.
Pizarro’s capture of Atahuallpa, then, explains why Europeans colonized the New World because it illustrates the ways in which the “guns, germs, and steel” gave Europeans advantages over the natives of the New World.