Why were there four parties and candidates in the providentially election of 1860?

The country was badly split in 1860 over slavery and the right of states to secede from the federal union , The Democrats basically split over these two related issues, The Republicans were a new party that was the most anti-slavery of the four. The fourth party was a party that took in the old Whigs who did not feel comfortable as Republicans.

In a nut shell, you might say that the old two party system became four because each party split in two over slavery and states rights.