John Q. Adams ran again to seek a 2nd term after being made president thanks to Anti-Jackson politicians in the House of Representatives.
Shortly after Adams term begun, Jackson was practically nominated with no challenger to take Adams on again. Adams was also nominated with no formal process.
The Democratic-Republican party by this time pretty much spilt in two. The ones who supported Jackson called themselves Democrats, and thus formed the party that stands today. Those who supported Adams became the National Republicans which later turned into the Whig Party.
Ironically Adam's Vice President John C. Calhoun did not become his running mate. He joined Jackson's ticket and became a Democrat.
Secretary of the Treasury Richard Rush became Adam's running mate.
This election marked the first major event of mudslinging in presidential politics. Adams' campaign pressed the issue of Jackson's marriage to his wife not being legal since there was trouble of getting a final divorce from her first marriage. Jackson's campaign fired back with accusations of governmental corruption committed personally by Adams.
Regardless of campaign tactics, it was a clear-cut victory for Jackson. Jackson carried 56% of the popular vote, 178 electoral votes, and 15 states. Adams had only 43.6% of the popular vote, 83 electoral votes, and carried only 9 states.