What developments deepened the divisions between north and south?

Well, first of all, I will answer this question as if you are talking about Northern and Southern United States, in specific, the Civil War. I apologize if this is not what you meant by North and South.

One of the most commonly given answers is, obviously, slavery. The south had slaves and the north had abolitionists (people who did not like slavery). And as such the north started to protest the actions of the south. The north started to provide safe haven for run away slaves from the south, and this rather displeased the south. The south viewed this as a direct affront to their rights as U.S. citizens, claiming that the slaves were their property and the north is stealing it.

Very quickly, the entire matter became one of rights, with the north saying that southern rights should not extend dominion over their slaves, and with the south saying that the north was being unconstitutional and tyrannical in attempting to take away their slaves. The south thought that if the north have a say on whether they can or cannot have slaves, then the north won't stop there.

The civil war then started when the south attempted to secede. At this point the war really wasn't about slavery at all, but about rights. The south wanted a country of their own to make their own laws, and the north wanted the United States to stay united.