The Langston Hughes poem "Harlem" is sometimes also entitled "A Dream Deferred." The most memorable line from the poem is as follows:
What happens to a dream deferred? / Does it dry up like a raisin in the sun?
As the previous educator mentioned, Lorraine Hansberry uses the simile between a dream and a raisin to explore how the Younger family's dreams and hopes often shrivel when confronted with certain realities, such as greed and dishonesty (e.g., Willy running off with Walter Lee's money for opening the liquor store) and racism (e.g., Mr. Lindner working to keep the family out of predominately white Clybourne Park).
Another possible reason for Hansberry choosing this title could be her desire to assert her place within a literary tradition. Hughes was a central figure in the Harlem Renaissance. He, like many Black artists in the 1920s and 1930s was cosmopolitan—he spent time living in Paris at the same time as the poet Claude McKay, the entertainer Josephine Baker, and the nightclub owner, Bricktop, whom Hughes helped to welcome to Paris when he worked as a cook at Le Grand Duc. Hughes was also a Communist sympathizer, though he never joined the Communist Party. Hansberry, too, became known in the early-1960s for her radical left-wing politics.
Traditionally, Black American literature, starting with the poetry of Phyllis Wheatley in the 1700s, has been inextricable from racial politics. Hansberry's career began shortly before the advent of the Black Arts Movement in 1965, which is also the year in which she died. One could argue that, without the contributions of writers like Hansberry and James Baldwin, who began working in the late-1940s and 1950s, respectively, the movement might not have occurred. It was Hansberry who began to push for a uniquely Black aesthetic and, with her final play Les Blancs (the title was influenced by Jean Genet's The Blacks), she also investigated the politics of liberation. These desires to seek a uniquely Black aesthetic and to push for Black liberation (think of Marcus Garvey's repatriation plan through the United Negro Improvement Association) began to be expressed during the Harlem Renaissance.
Thus, I would argue that Hansberry chooses her title, not only because it is apt in describing the how racism causes ripe dreams to dry up, but also because her nod to Hughes establishes her within a tradition that continued to use literature to investigate the problems of racism and economic oppression.