I am assuming that you are referring to the party system that existed in the time leading up to the Civil War. This was the one that had the Democrats opposing the Whigs and which eventually broke down as the Whig Party split over the issue of slavery, as described in the link below.
The impetus for the creation of this party system was the fact that there were splits arising between the "common people" and the richer elites. The common people moved towards the Democratic Party during the Jacksonian Era and the elites set up the Whig Party. The Democrats wanted more democracy and they disliked big businesses and high tariffs. The Whigs wanted the government to work to improve the economy and to help manufacturing.
This party system broke down in the 1850s as the issue of slavery split the Whigs into Northern and Southern wings.