What principal factors accounted for the explosive growth of cotton production and slave labor in the South in the 1850's?
There were at least three principal factors that allowed this to happen.
First, there was Eli Whitney's cotton gin. The invention of this machine allowed the efficient cleaning of short-staple cotton such as could be grown in the South. This allowed a boom in cotton production and slave labor.
Second, there was the Industrial Revolution. The mechanization of the textile industry in Britain and the United States led to much more demand for cotton than there ever had been before. Greater demand meant that more people would want to grow more cotton using more slaves.
Third, there were improvements in transportation. With better shipping and railroads, it became easier to move goods from place to place. This expanded the market in which Southern cotton could be sold.
In these ways, the demand for cotton rose, the supply of cotton rose, and it became easier to get cotton from supplier to customer. These factors caused a boom in Southern cotton.