The phrase 'Manifest Destiny' has been used many times throughout the history of the United States, and with many different meanings attached to it. The term was first coined by American journalist John L. O'Sullivan in his piece 'Annexation', written for the Democratic Review in 1845 to urge the annexation of Texas. (Annexation). The second use of the term by O'Sullivan is part of an argument in favor of "the whole Oregon", an expansionistic viewpoint in reaction to a boundary dispute over the Oregon Territory between the United States and Great Britain. The term doesn't enter general political usage until it is derided in Congress by his opponents.(wikipedia.org)
Because the term survived several decades of use, it is often imprecise to define what is meant by 'Manifest Destiny' unless it is applied to specific times and situations (such as Manifest Destiny as an attitude toward the Native Americans at different times and places during the westward expansionistic sweep). Still, there are some general similarities to all of the attitudes which have sprung forth under Manifest Destiny.
First and foremost, it holds that there is some moral virtue, something special and exceptional, in the American political and cultural system — the 'Anglo-American'/'white' culture and political system. It then holds that God or Providence has given to the American people a special destiny, defined differently by time period and speaker, but most commonly referenced as an expansionistic destiny that America would rule 'from sea to shining sea'. And finally that as the virtue of our way of life spread, our destiny would be made manifest on earth.