Before the Civil War, the Northern and Southern states were very different places.
The Northern states were mostly industrial. Their economy relied mostly on factories that produced textiles, shoes, tools, and other goods. There were some farms in the North, but they were mostly smaller farms. The Northern states felt that slavery was wrong and should be ended.
The Southern states were mostly agricultural. That means that their economy was dependent on growing and selling crops. Slaves were used to plant and harvest the South's most important crop - cotton. Many Southerners worried that an end to slavery would destroy the South's economy. They felt that if the federal government passed a law that the states did not like (getting rid of slavery, for example) then the states should have the right to not obey it. This feeling that the states should have the final decision was referred to as "states' rights."
After several events that created even more tension between the North and the South, a war broke out between the two groups. There's a lot more to the story, but that's what you're going to have to find out in the next couple of weeks.