How does using a road as a symbol for his experiences affect the meaning of Martin Luther King, Jr.'s Nobel Peace Prize acceptance speech?

As George Lakoff describes in his 2013 essay called "Why it's Hard to Replace the 'Fiscal Cliff' Metaphor," spatial metaphors take an especially strong hold on the human imagination because they are easy to visualize.
A metaphor is a comparison that does not use the words like or as. King's use of the term road is a metaphor. He is comparing his work of achieving a Nobel prize to traveling on a "tortuous road." This metaphor acts as a symbol because it represents an idea, in this case the idea of a journey that has a purpose and end.
"Road" is potent because, as said above, we can visualize it. It is also a common, everyday symbol: almost everybody has been on a road of some sort. It is an inclusive symbol, too. As King notes, many people can travel on a road and on the same road he travels.
Most importantly, a road leads to a destination. King has an end in mind for the Civil Rights movement. The movement comes closer to that end when a person like him earns the visibility and respect of a Nobel Prize, but that is only one stop in the pilgrimage to equal rights for all African Americans.

In the speech Dr. King gave when accepting the 1964 Nobel Peace Prize, he said,

"The tortuous road which has led from Montgomery, Alabama to Oslo bears witness to this truth. This is a road over which millions of Negroes are traveling to find a new sense of dignity."

As he made the speech, events were still unfolding in the United States, including the relatively recent murder of civil rights activists in Mississippi. By using the symbol of the road, Dr. King emphasized the progress his movement had achieved while acknowledging the continued progress the movement had to make. The image of the road conveyed both of these ideas at the same time so that the audience could feel jubilant about events such as the successful 1955-1956 Montgomery bus boycott and the Civil Rights Act of 1964 while also understanding Dr. King and his movement were still committed to ongoing work on a campaign that had not yet achieved all its goals. The symbol of the road allowed Dr. King to be celebratory and urge his audience to support his continued work for civil rights.