The major strength of the "Cotton Kingdom" was that it was lucrative. The cultivation of cotton was able to create a large number of wealthy plantation owners and to serve as the backbone of the entire Southern economy. The cotton economy was also very important to the North as many northern companies relied on doing things like selling insurance to Southerners.
There are at least two weaknesses of the system (outside of the fact that it was immoral). First, it left the South as something of a colony, exporting cheap raw materials and importing finished goods of all sorts. Second, it made it harder for the South to diversity its economy and to progress. Too much of the South's wealth was tied up in slaves, meaning that it would be very difficult for manufacturing and commerce to become important contributors to the Southern economy.
The pre-Civil War South had turned itself, over nearly two and a half centuries of plantation agriculture and slavery, into the supplier for the world's textile industries and brought serious wealth to the privileged few who happened to own those plantations. "King Cotton" was a common nickname given to the new economy that cash crop had developed in the southern states. This gave those states leverage in national and world affairs, and created the wealth which gave the South the impression it could make it on its own.
However, that economy was seriously one-dimensional, and as the rest of the country and Europe was industrializing at a rapid pace, the South was more dependent on cotton revenues than ever. Plantation agriculture also did not, by nature, attract many immigrants to the South, so the fact they relied on cotton for income limited the South's population growth outside of slaves. This was a crucial factor in the oncoming Civil War.
So it's fair to say that cotton gave the South wealth, confidence and identity, but also was its eventual undoing.