During the Harlem Renaissance, it became fashionable for the wealthy whites of New York to visit The Cotton Club and other such jazz and blues establishments. This merging of the rich in an area where they hitherto would not have ventured brought to their consciousness "the Negro Problem" that there were many black people who had moved to New York.
Since it was considered fashionable to go to the Harlem nightclubs, it also became fashionable to talk of this awareness of the influx of African-Americans from the South. However, as Hughes portrays in his poem, it is only dinner conversation "in current democratic night"--the daytime would return things to the status quo of separation of black from white. As the guests eat wild strawberries which are also imported for the dinner [the correct phrase is fraises des bois, so perhaps Hughes puns upon the name W.E.B. Du Bois here], there is little reality to this conversaion on Park Avenue as one guests observes, "I'm so ashamed of being white" as the appropriate and polite thing to say for this "democratic night."
Even the poet realizes that he is the curiosity for the night, "the center of attention," at least the "Problem" has been brought up. And, perhaps, the next step is a "Solution." It will, however, have to wait some time as people now just complacently return to the security of their wealth and social status.