Hughes has a consistent theme of freedom and equality in much of his poetry, and that theme is evident in these three poems. He speaks of dreams, and the common dream that he shares in these poems is his dream to one day be equal, to be able to walk tall and proud with all other humans on this earth, even if he is black. In "Dream Variations" this sentiment is expressed through these lines:
"That is my dream!/To fling my arms wide/In the face of the sun,/Dance! Whirl! Whirl!/Till the quick day is done./Rest at pale evening . . ./A tall, slim tree . . . /Night coming tenderly/Black like me."
He desires to be able to, in the sunshine (in the open, in society) to be able to "dance" (or be himself, treated equally, not having to worry about what others think of him) and then to "rest" like everyone else, with no worries, and be proud of being black (since, after all, the night-a natural phenomenon-is black too).
In "Let America Be America Again" he expresses his desire for equality-not only for blacks, but for all the downtrodden in America-in these lines:
"O, let America be America again--/The land that never has been yet--/And yet must be--the land where every man is free./The land that's mine--the poor man's, Indian's, Negro's, ME--/Who made America"
and he goes on to say that they must take America back and make it be that beautiful place of shining equality again. In "Harlem," that dream isn't expressed as explicitly. Instead, he refers to the fact that they must take this dream and make it come true, now, before it dries, festers, stinks, crusts, or explodes. He askes, "what happens to a dream deferred," meaning, a dream put off or not realized. The ugly similies and word choices he uses to describe a dream just sitting there not being realized are repugnant enough to encourage anyone to take up their dreams, and make them come true.
I hope that these thoughts help; I provided links to all three poems in case you need them. Good luck!