Assuming this is referring to the Manifest Destiny painting (American Progress), the woman is facing West (the direction that the country is expanding, which is dark and undeveloped as of the time period). The woman is Columbia, and she represents the United States. This relates to manifest destiny as the lady moving West symbolizes the US expanding towards the West, furthering the idea that the nation had a divine right to settle the continent from coast to coast, thereby moving to the darker, unexplored territories.