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.
Does it stink like rotten meat? (6)
Rotten meat stinks up the fridge when we don't eat it soon enough or when forget to throw it out, or it can stick up the kitchen when we forget to take the trash out. Choosing not to eat the meat soon enough will create a smelly situation later on. Choosing not to act on your dreams will lead to a sticky situation later on.
Or does it explode? (11)
Our speaker suggests that deferring dreams can be a dangerous enterprise. Do you feel like the verb "explode" could have a positive meaning too? The fact that this line is italicized makes us feel like it is a very special line, and it also makes us feel like our speaker is kind of excited about what he is saying here. Even though we know that bombs explode, we also think of fireworks exploding too.