The correct answer is: The image shows the impressive potential of a just society.
Indeed, the lines come from his 1963 I have a dream speech: “But there is something that I must say to my people who stand on the warm threshold which leads into the palace of justice. In the process of gaining our rightful place we must not be guilty of wrongful deeds. Let us not seek to satisfy our thirst for freedom by drinking from the cup of bitterness and hatred.”
The imagery lies on very Western, Judeo-Christian imagery: royalty, nobility, monarchy. Dr. King was a very educated man. The metaphor of a threshold is related to the notion of the heavenly Jerusalem. However this Jerusalem is not only religious but political, it is the America that is yet to be. This Jerusalem is imperfect because it keeps a part of its own people outside of it, in the cold. This is also a very gospel theme, as African-Americans saw themselves as the new Jews who were looking to go back to their Holy Land.
Also, the palace image helps to convey the idea that African Americans had been oppressed by a monarchic regime, which had the power of life and death over them. Masterfully, King draws a parallel between racial and class injustice; and the notion is also historical: America became a free country after breaking with a tyrannical monarch. In this manner King reminds Americans that slavery was a betrayal of the principles of the American Revolution.