An old back room filled with clutter? That's not usually the stuff that poems are made of, is it? Well, if you happen to be cataloging the lives of two elderly people living in poverty, it turns out that this room is about all you've got to work with.
If you read closely, you'll notice that the room is actually a rented room – which is pretty unfortunate. See, these people don't own anything other than the scraps and cigar ashes, which clutter their room. Even their room isn't actually their own. We're not sure, but we're guessing that Brooks is making a subtle reference here to one of the on-going social problems in America: blacks, the descendents of former slaves, have historically lacked the inherited wealth that whites passed on to each other through the generations. There just weren't all that many black families that had houses passed on to them from their parents – or anything at all passed on. Couple the lack of inherited wealth with pay inequity and overall social discrimination, and you've got a recipe for poverty. As depicted in a small rented back room.
Of course, the poem itself doesn't say that explicitly. But then again, who would appreciate a poem that didn't require a little thinking on the part of the reader?