What happens to a dream deferred? (1)
The inversion in the phrase "a dream deferred" (as opposed to "a deferred dream) makes us think that the speaker is commenting on people whose dreams have been deferred against their will (rather than choosing to defer their dreams). There's something very passive about the word "deferred" that suggests to us that someone is doing the dreaming, and someone else is causing the delay.
Does it dry up like a raisin in the sun? (2-3)
This line makes us think of a raisin that has fallen out of our lunch bag and is sitting on the lunch bench in the hot sun, growing smaller and drier by the minute.
Or fester like a sore– And then run? (4-5)
Sores fester and run when we don't take care of them, when we pick at them, get dirt in them, and forget to put medicine on them. This line makes us think of someone choosing to let a wound get infected rather than choosing to take care of it.