The main thing that the presidential election of 1860 showed was that the United States was a country that was irreparably split along regional lines. This made secession and the Civil War essentially inevitable.
In the election of 1860, there were four major candidates. Two of these candidates came from the Democratic Party. This party could not decide upon a candidate that would be acceptable to all of its members. Instead, the Democrats from the South nominated one candidate while the Democrats from the North nominated another candidate. This disunity even within a single political party helped to show the depth of the problem.
The results of the election also showed this problem. The Republican candidate, Abraham Lincoln, was elected without even being on the ballot in the South. This meant that the country was so divided that a president could be elected without getting any votes in an entire region of the country. This was extremely bad because it made clear that the country would not be able to remain united.