Sounder
Sounder is the only character in the novel called by name. The rest are referred to generically by what they are: “the boy” or “the Sheriff” for instance. This is ironic symbolism as well as personification: Sounder is the representative for all the finer aspects of humanity, of course, but in a way in which the ability to appreciate those traits in a dog says quite a bit about the ways humans treat other humans.
The Book
The book of philosophical essays which the boy finds discarded in the garbage and must furtively retrieve for himself is symbolic of the institutionalized racism of the American educational system. At first, slaves were forbidden to read. Then with emancipation they were forbidden to attend school. At every turn, white society has made it hard for blacks to become educated even as many of them squandered the opportunities made freely available to whites by either literally or metaphorically throwing books into the garbage rather than letting anyone with black hands get their fingers on them.
David
The biblical story of the scrawny young shepherd who defied the odds by taking down the mighty Goliath and rising to become King of Israel is the symbol of possibility for the boy. David is proof that even against the mightiest of odds, underdogs can sometimes win.
Curtains
The only houses with curtains that the boy has ever seen are those belonging to the wealthier white residents. The curtains become a symbol of multiple layers. The fact that only the white people living in big houses have them is a sign of economic inequality; you have to have money to afford them and you have to be white to have money. But the curtains do not entice as a symbol of luxury, rather they instill a sense of fear and dread in the boy because one can’t see through them. Therefore, you can never know if you are being watched by someone inside a house with curtains and in this way they become symbols of black fear of white power conspiring against them.