How did social life develop in the South between 1830 and 1860 as a result of dependence on cotton?
Because the cotton gin was highly efficient and slavery made the cost of producing cotton (from the owner's perspective) artificially cheap, cotton was a highly profitable industry, more than it really should have been if workers had been free to choose other jobs.
As a result, almost all of the investment in the South during this period (what we now call "antebellum," meaning "before the war") was in cotton production; while the North had a diversified economy with many agricultural products as well as industrial manufacturing, the South became almost entirely dependent upon cotton exports for its whole economy---and hence, on slavery.
Without the need for skilled engineers and factory workers, there was little incentive to invest in education; so literacy rates were low. Cotton was profitable enough on its own, so aside from some minor improvements in the cotton gin there was little incentive to invest in technology.
Inequality in the South was extraordinarily high. Of course there were the slaves themselves, who owned next to nothing; but the majority of the population was quite poor as well, as the wealth from selling slave-picked cotton was funneled upward into a small number of rich families. This concentrated wealth came with concentrated power, and the plantation owners essentially ran the government.
Besides being obviously unjust, this economic and social system was also extremely inefficient; the South lagged behind the North economically because of the unwillingness of Southern elites to transition away from slave-based cotton plantations to more productive industries. Yet the elites themselves were doing quite well under the current system, so they had little reason to change, and fiercely resisted not only the abolition of slavery but also the establishment of new industries. This state of affairs likely would have continued for decades more, had not the conflict over slavery with the North erupted in the Civil War.
Here's a link to a book on the antebellum South; it goes into a lot more detail about how slavery and its associated institutions influenced almost everyone's way of life.