What caused the sectional divide that confronted the nation on the eve of the Civil War?

The most obvious answer would be slavery. Southern society and its economy were based upon what was euphemistically described as "the peculiar institution." On the whole, public opinion in the North was incredibly hostile towards slavery, and Lincoln's pledge to resist its extension formed a key plank of his platform in the election of 1860.
But the deep sectional divides between North and South went back much further in time than that election. To some extent, they were formed over the better part of a century, emerging out of the unresolved struggle over the American Revolution's political legacy. The Southern states were the descendants of Jeffersonian Republicans—not to be confused with the Republican Party of Lincoln.
The Jeffersonian heritage emphasized the ultimate sovereignty of the states, with a corresponding suspicion of centralized federal government. Though Jefferson was acutely aware of the iniquities of slavery—despite being a slave owner himself—he believed that it was a matter for the states not the federal government. Jeffersonian Republicans were intensely suspicious of anything that smacked of overreach by the federal government, and this attitude remained deeply embedded within the South's collective psyche.
The Southern economy also exemplified the Jeffersonian ideal. It was an agrarian economy, its wealth generated from the land; cotton was the principle cash crop. Although there was some industry, it had nothing like the same degree of significance as in the North. This relative industrial backwardness proved to be a serious handicap to the South in waging war. Yet the old attitude persisted in the South that land was a more reliable source of wealth than commerce or industry. Besides, so long as slavery persisted, there was little or no incentive to diversify the economy.
The Northern states had inherited the tradition of Federalism, whose crowning achievement was the Constitution. With its strong, centralized government and a modern economy based on finance, trade, and industry, the North exemplified the governing ideals of the likes of John Adams and Alexander Hamilton. According to the Federalist vision, political sovereignty needed to reside at the center. The states still had considerable authority in their own right, but matters between states ought to be dealt with by the government in Washington, DC, and slavery was one such matter.
Although the Federalist vision had prevailed at Philadelphia in 1787, the considerable tensions it had generated were never fully resolved. That it would take a Civil War to provide some kind of resolution bears eloquent testimony to just how deep were the sectional divides between North and South and their radically different understandings of how American government should be organized.