This is a complicated and controversial question. I would argue that the two sides initially were fighting over the issue of states' rights. However, it is important to realize that one of the most prominent states' rights in question was the right to hold slaves.
The South clearly was fighting over states' rights. They wanted to guaranteed right to run their states as they wished. One of the most important rights on their list was the right to own slaves. However, they did also care about other issues, as was seen in the controversy over the tariff in the late 1820s and early 1830s.
The North was fighting largely to defeat the South's view that the states should have expansive rights. The North wanted to preserve the Union with a strong central government. They were not trying to end slavery just as most Northerners before the war were not in favor of abolishing slavery in the South.
The war started out, then, as a war over the degree to which states would have autonomy. However, slavery was a major issue in the debate over autonomy.