The fact that the people of the Fertile Crescent were the first to domesticate many plants, especially cereals, gave it a tremendous head start on the rest of the world because it enabled the development of agriculture. Agriculture led to a settled, sedentary lifestyle with a dependable food supply. This, in turn, led to many of the hallmarks of modern societies, including complex technology, social stratification, and other important developments. Because of the long east-west axis of Eurasia (which meant much of the landmass was along a similar climate zone) the spread of domesticated plants and animals necessary for agriculture happened pretty quickly.
Virtually all of the societal developments that allowed Eurasians to dominate other peoples came, in short, the "guns, germs, and steel" from which the book derives its name, stemmed from the development of settled agriculture:
Much of human history has consisted of unequal conflicts between the haves and the have-nots: between peoples with farmer power and those without it, or between those who acquired it at different times.
Diamond's essential point is that these developments proceeded not from some inherent intellectual superiority among Eurasians, but rather from geographical accident. The Fertile Crescent was the earliest location for agriculture because there were so many domesticable plants and animals there naturally.
Source: Diamond, Guns, Germs, and Steel, 93.