The term “Great American Desert” is one that was used in the 1800s to refer to what we now call the “High Plains.” This is an area that is generally between the Rocky Mountains and the 100th Meridian. The 100th Meridian runs north to south from the Dakotas and down through Texas. It is generally seen as the dividing line between the Midwest, which gets relatively large amounts of rain, and the West, which does not.
When people called this area a “desert” they did not mean that it had sand and sagebrush and cactus. Instead, they simply meant that it did not have trees and did not seem to be good for farming. The Great American Desert did not get enough rain to make it very suitable for farming without irrigation. When irrigated, much of the area is very good for farming. In the days of westward expansion, it was a relatively dry area of steppe and grassland.