The idea or term manifest destiny refers to the push for Westward Expansion in America during the 1830s and 1840s. People believed it was our divine right to spread across the continent because our ideals of freedom, liberty, and democracy should be extended to all people. The politics during this time centered around Texas (won from Mexico in the Mexican-American war), California, and Oregon (through negotiations with the British).
Politically there were two camps. Those that did not think westward expansion was a good idea because they felt they would have less influence in national affairs and those that thought it was a good thing. The Democrats used this idea to really create party unity and were generally in favor of Westward Expansion. Later other parties got on board with this idea and used it as part of their platforms.
One big issue was - slavery - should it be allowed in the new territories. This was the topic of much debate and several laws allowing or abolishing it.
Another issue was the fear of threats from other countries - mainly France.