Man The fertile crescent is awesome, I love it! I'm so glad you asked. First off, the Tigris and Euphrates flood all the time. When they flood, not only do they bring water further out and essentially irrigate the land far away from the river, they also bring all this incredibly fertile soil up from the river bed that gets spread out all along the river which is great for early agriculture before people discover fertilizer or irrigation.

Secondly, the fertile crescent is pretty close to Africa, that big continent where people come from. People where already building a civilization in the fertile crescent before anyone had set foot on either of the Americas, so just in terms of physical proximity the fertile crescent had a huge headstart. Also, most of Africa is pretty bad for agriculture due to viruses, diseases, lack of rain or too much rain. The most notable exception is the Nile river, which is pretty darn close to the fertile crescent.

The third reason is that everything early people needed was there. There are a whole bunch of plants that the early settlers of the fertile crescent had access to including Barley, Wheat, Peas and Lentils, all of which are such good foods that they are staples around the world. Also, all of the typical "farm animals" (Cows, Pigs, Sheep and Goats) that are incredibly important to agricultural development were abundant in the region. Basically, the fertile crescent had everything early people would need to start agriculture without knowing anything about agriculture. The rivers irrigated and fertilized the land, the wildlife already grew there and only needed to be harvested and controlled, and the fauna was ripe and easily tamed to provide milk, meat and labor for further development. Hope This Helped!