A combination of a dry, windy weather pattern (aka a sustained drought) and poor farming practices. Because people didn't understand the value of crop rotation at the time the nutrients in the soil were used up and the plants that were planted had little to survive on. So you have plants that were already dying going through a drought. When the wind kicked up it just blew the dirt around because there were no plant life to hold it in place.
The phenomenon was caused by severe drought combined with farming methods that did not include crop rotation, fallow fields, cover crops, soil terracing and wind-breaking trees to prevent wind erosion.