The desert belt can best be described as the air that moves around the equator. Specifically, air that is going up or rising is pushed out from the other air below it. Due to this change, the air is cooler based on the air that is coming from the higher altitudes. That air would be cooler and it is replacing the hot air around the equator.
The main reasons for the formation of African and Eurasian desert belt is because it is located in the sub-tropical high pressure cells. It is under the influence of warm ocean currents. There are also desert belts in other areas of the world including in the United States and in South America. These places have the changes of air.