The Fertile Crescent has a Mediterranean climate that features mild winters with lots of rainfall and hot, dry summers. This selects for plants that put most of their energy into making large seeds, some of which are edible and nutritious. Many of the world's most widely cultivated cereals are indigenous to the Fertile Crescent, which actually lies within the world's largest zone of Mediterranean climate. Additionally, the natural ancestors of these cereals, including wheat and barley, were already present in the wild, and required very little domestication. Another advantage is that many of the important plants of the Fertile Crescent were self-pollinating, which made them easier to domesticate. Additionally, there are a very broad variety of geographic areas within the Fertile Crescent, which led to a broader range of plants and animals for domestication. Finally, the region's incipient farmers had less competition from hunter-gathering peoples.
Source: Diamond, Guns, Germs and Steel, 142-144.