Manifest Destiny came about in the 1840s, but it was really a new name for an age-old concept, and one which was very common to the nations that were predecessors to America. England, Portugal, Spain, the Netherlands, Italy, and the rest of Europe were all very familiar with conquest.
There was a divine right of kings that England adhered to that eventually grew into colonialism, and Manifest Destiny was very similar. Manifest Destiny essentially claimed that the nation of America had the rights to the entirety of the North American continent, "from sea to shining sea." Once the settlers had ousted England, they began to venture further west and claimed more and more territory. Eventually it got to the point where, upon defeating Mexico in the Mexican-American war, they felt entitled to the entire continent. Essentially, they believed that God had given them the continent and that it was theirs to take and rule.
This is the same concept exercised by the old nations of colonial times and was simply a conqueror's mentality rebranded.