There was a rush for land in the years leading up to the Great Depression, as a new strain of Russian Thistle Wheat was found to grow very well on the Plains, and the aquifer of water there was tapped to irrigate thousands of new farms. World War I and the economic boom of the 1920s had caused a surge in demand for wheat, so prices were high and prospective farmers struck out for places like Oklahoma and Kansas to become "sodbusters": people who broke up the centuries old natural turf of the Plains in order to farm it.
The post above is exactly right when it talks about how disastrous it was to remove this natural sod because it took hundreds of years to form and could not be replaced. But another very important and serious cause of the problems farmers faced during the Depression was overproduction and low prices. Too many people became wheat farmers, the price of wheat went through the floor, and farmers went belly up, unable to even pay their debts. When the wheat was not replanted on their vacant farms, the bare Earth was open to both drought and windstorms and literally blew away.
For a great resource on this subject, check out Timothy Egan's book The Worst Hard Time. He tells some stories about what happened to farmers in that time that are almost unbelievable. You can listen to him read some on National Public Radio, as well as read some excerpts yourself by following the link below.
The major problem that farmers in the Great Plains faced during the Depression is known as the "Dust Bowl." This problem was caused by two main things:
First, the problem was caused by nature. The 1930s were a time of really terrible drought on the Great Plains. This, of course, made the soil drier and more likely to blow away.
In addition, there was a problem that was caused by human beings. For the last few decades, farmers had been changing the environment. They had been removing the native prairie and replacing it with farm fields. The farm fields did not naturally hold the soil together (preventing wind erosion) the way that the prairie had.
When the man-made problems combined with the drought, huge dust storms became possible. This was the cause of the Dust Bowl that was such a problem for farmers on the Great Plains during this time.