The exact definition of Manifest Destiny is a bit murky, because it was never a specific policy or philosophy with a list of ideals or criteria. It is, in retrospect, more of an aggregate term for the zeitgeist of early 1800s American thinking.
Manifest Destiny was, at its core, an expansionist policy. Moreover, this expansionism was in some sense "blessed". The exact extent of this policy, and the nature and origin of the blessing changed depending upon the time and the parties involved; it might be likened to a philosophical cousin of the Crusades. In brief, it stated that the American way of life was destined to spread throughout the continent, and that this was a good thing because the American way was virtuous.
This concept evolved significantly over time; for example, it is largely responsible for many of the large territory gains made by the United States in the 1800s, such as the Louisiana Purchase and the gains of the Mexican-American War. Later, when America came under scrutiny for imperialist ambitions, the concept of Manifest Destiny was nudged in the direction of America being a peacekeeping guardian of democracy and insulation from European interference for the entire Western Hemisphere.
Manifest Destiny has significant conceptual ties to the concepts of American Exceptionalism (there is something unique and good about America) and the White Man's Burden (that white men and white culture is bound by moral obligation to civilize the nonwhite races).