One of the purposes of poetry is to open up possibilities in the reader's mind, to get the person to think about something. This would be very important in Langston Hughes' context, being an African American writer at a time when racism was seriously overt. He was writing at the time of Jim Crow laws and even restrictions of African Americans in northern cities.
A Dream Deferred covers the difficult realities of so many African American people. Much like today, many had little hope for their lives, certainly not the hopes of the wealthy (mostly whites) who can go to college and choose to focus on something they like. Young people with ambition were and are regularly forced to abandon such dreams.
When African Americans read the poem, they may find that it speaks to their lives and conditions. Hughes' white readers might off-handedly reject the poem because its realities are bitter. By asking questions, Hughes makes a bitter pill a little easier to swallow.
At the same time, the questions communicate something truly significant. Why have there been protests and riots that began some time after Hughes was writing and continue today with Black Lives Matter? Hughes' answer is that this is what happens when dreams are deferred. The next question readers have to ask themselves is, how can I be part of a solution rather than being part of the problem? How can we help people to realize their dreams?