The tensions over the slavery caused conflict in America primarily because of the different political views on the matter, as well as the economy.
The North wanted to modernize, and to follow the example of the European countries that abolished the slavery, thus they wanted the slaves to be freed, and to be equal citizens in the society. Also, the North was industrialized, so they were really not dependent on slaves to keep their economy going.
The South wanted things to remain the same. They did not wanted the slavery to be abolished, but instead to remain as it is. The economy of the south was largely based on the plantations with different types of crops. Big portion of the work done on the plantations was done by the slaves, so if they were freed, that would mean that the plantations would either be left without enough laborers, or the former slaves would have demanded wages that would lower the profit of the plantation owners.
This disagreements eventually led to a bloody conflict, which ended up with a win for the North.
