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.