The main question of Langston Hughes' "Harlem" is "What happens to a dream deferred?"
The question is asking, what happens when someone's dream is put off, delayed or postponed?
As this is the first line of the poem, it is safe to assume that this is a key element to the poem's meaning, and that it is not a casual inquiry. In other words, the reader can assume that the "dream deferred" is something extremely important.
Hughes' father was uncomfortable with his racial heritage. Hughes, a black man, experienced racial prejudice at Columbia University and left because of it.
We know that Hughes was alive during the Civil Rights Movement. Hughes wrote, "Let America be America again. Let it be the dream it used to be." The Civil Rights Act was signed in 1964. Hughes died in 1967.
With all of these things in mind, the "dream" may refer to the "American dream," where freedom and prosperity were supposed to be available to all people. Or, the "dream" may refer to Martin Luther King, Jr.'s dream of equality for all men, regardless of race.
With the assumption that the dream is the most important thing, the question remains, what happens when that dream is not attainable?
The two alternatives offered in the poem are opposites: drying up or exploding; shriveling to nothing or bursting violently. I believe that these two lines, opposites, offer the potential reaction of a person whose dream has not been realized, and that Hughes believes there is fine line between the two manners in which a person will react.
Additionally, the other descriptions between the two extremes are quiet and unhealthy, but not violent. Perhaps Hughes is suggesting that a dream unfulfilled may linger and torture in many cases, but for some, the disappointment cannot be contained and will not "go quietly."