The Dream to which Coates refers throughout his book is the American Dream, that great American mythology of freedom, prosperity, and upward mobility. But like any myth, the Dream exists within its context, within the history of this country, and through this history the Dream is shown to be a delusion. Every American does not have the same access to the Dream, and the deluded belief that we do—if we only work hard enough we will be rewarded—keeps the Dream persisting to this day.
The people that Coates calls Dreamers are the people who hold on to this deluded belief in the Dream. Mostly, he uses it to refer to people of color (particularly black people) who believe that because they have achieved typical markings of the Dream (that "fantasy of suburban prosperity" that Jules mentions here), that means it is right and true and attainable for everyone. Near the end of the book, Coates says:
The Dreamers will have to learn to struggle themselves, to understand that the field for their Dream, the stage where they have painted themselves white, is the deathbed of us all.
It also must be mentioned that any book which is speaking on race in America and speaks of "the Dream" is alluding in some way to Martin Luther King Jr. and his most famous speech "I Have A Dream." In our current social climate, this reference back to the lineage of American voices on race is a reminder of how little has changed in the fifty years since MLK gave that speech. MLK refers to police brutality, ghettoization, and voter suppression. And then he says:
I say to you today, my friends, though, even though we face the difficulties of today and tomorrow, I still have a dream. It is a dream deeply rooted in the American dream. I have a dream that one day this nation will rise up, live out the true meaning of its creed: "We hold these truths to be self-evident, that all men are created equal."
I have a dream that one day every valley shall be exalted, every hill and mountain shall be made low.
In the first quote, MLK directly references the American dream, but distinguishes his own dream from it. There is something beyond that American dream that he believes America must strive for. In its current form it is not inclusive of all Americans. He expresses hope that one day America will be able to fulfill the promise it made at the beginning: a true equality for all.
But in the second quote (which is a biblical illusion, because he was a pastor), he seems to imply that a radical change is needed—not an opening of a door by white people, to allow people of color inside. Instead it must be an agreement by those both inside and outside, that maybe the entire structure needs to come down and be rebuilt.
Toward the end of "Between the World and Me," Coates refers to his return to Howard for Homecoming and describes something akin to what MLK may have been referring:
That was a moment, a joyous moment, beyond the Dream—a moment imbued by a power more gorgeous than any voting rights bill... The power is not divinity but a deep knowledge of how fragile everything—even the Dream, especially the Dream—really is.
From one great intellectual activist to another, runs an underlying current of hope, that there could be a future beyond the fragile Dream, where something else entirely can be built.