Interestingly, slavery wasn't the biggest issue in question at the start of the Civil War. The main conflict that sparked the war was the Confederate attack on Fort Sumter in 1861. After this attack, the Confederacy seceded from the Union and formed its own nation to engage in battle with the Union.

The underlying issues, however, were much more complex. Slavery was a hot-button issue, particularly in regard to the new territories being added—there was great debate over whether slavery should be allowed in new territories. However, also at the heart of the issue was the complex debate over state's rights. The Confederacy was dedicated to the rights of the states more so than the control of the federal government, and they clung to their state-given right to continue practicing slavery. They believed that, by legislating where slavery was legal and illegal, the federal government was taking power away from the states and was therefore overstepping its boundaries.

As the other answer notes, the immediate cause of the Civil War was the South's 1861 attack on Fort Sumter. This attack was in turn motivated by the election in 1860 of President Abraham Lincoln, a candidate Southerners feared and despised.

More deeply, as mentioned in the other response, slavery was the cause of the conflict. Over the course of the nineteenth century, positions on slavery had gradually polarized. If the century opened with both Northerners and Southerners more or less of one mind in seeing slavery as an institution that would gradually wither on the vine, by the 1850s that consensus had utterly broken down. Especially after the publication of Harriet Beecher Stowe's novel Uncle Tom's Cabin, which outlined the horrors of slavery, people in the north raised a louder and louder outcry for the immediate end to slavery. Meanwhile, Southern leaders hardened into insisting that slavery was actually a good institution that needed to be preserved and expanded, not a necessary evil.

As the two ideologies diverged, war became more and more inevitable. Beneath slavery too, as historian Bruce Catton has pointed out, lay a deeper divide in worldview: the South was agrarian, backward-looking, and hierarchical in its ideas of how society should be organized while the North was increasingly industrial, forward-looking, and equalitarian in its concept of society.

The immediate cause of the Civil War was the attack on Fort Sumter by Confederate batteries in April of 1861. This led Abraham Lincoln to issue a call for troops to crush the rebellion, which in turn caused Virginia, Tennessee, North Carolina, and Arkansas to secede from the Union. After this event, the Civil War was on. 

The underlying causes of the war were more complex, but can be traced to the divisive issue of slavery. Long a simmering issue, it became particularly toxic in the aftermath of the Mexican War, which raised the question of the expansion of slavery into the western territories. This political issue was increasing powered by the moral force of the abolitionist movement in the North. While most...