Symbolism, Imagery, Allegory
Given that dust is in the title and shows up in pretty much every chapter, it's obviously pretty important to this book. You could even argue that it's kind of a character in the story, a sinister, destructive presence that blows into the characters' lives to mess things up.
In particular, Billie Jo and Daddy spend a lot of time fighting against the dust's ill effects. The dust destroys Daddy's efforts to grow wheat, repeatedly forcing him to start over, and he literally runs into a dust storm in an insane attempt to confront it, even though he has to know on some level that "you can't stop dust" (17.5). Heck, if it wants to, it'll swarm into your house—no matter what measure you take to try to stop it.
Check out this frightening encounter Billie Jo has as she journeys home from the movies in a storm:
Brown earth rained down / from sky. / I could not catch my breath / the way the dust pressed on my chest / and wouldn't stop. / The dirt blew down so thick / it scratched my eyes. (75.5)
This says a lot about the role the dust plays in the characters' environment—it makes it hard to live, breath, and even see things clearly. True, it isn't always blowing this hard and it isn't always this painful, but still—the characters live with the constant threat of its return. Add into the mix that it makes farming virtually impossible at times, and the presence of dust becomes an existential threat.
The bottom line is this: Whenever any character—be it Daddy, Mr. Hardly, or Joe De La Flor—takes a step forward to recovery, the dust never fails to set them two steps back. Because of this, it's actually more than just a symbol—it fits the classic definition of an antagonist, the character that keeps the main character from getting what he or she wants. Except instead of just getting in Billie Jo's wait time and again—which dust most certainly does—it antagonizes the whole community.
You know what else antagonizes the whole community? Yup—the Great Depression. Because of this, dust doesn't just symbolize hardship in general, it symbolizes the crushing blow dealt by the economic crash. While any particular dust storm creates its own set of problems, ranging from sand in the dinner food to ruining most of a store's inventory, the relentlessness with which it returns makes it inescapable in a major way, just like the poverty bearing down on not just Billie Jo and her family, but the entire nation at this time.
The literal dust also provides the backdrop to the symbolic "dust" of the characters' lives—the things they would wipe away if they could. It makes the bleak circumstances of the farm's failure, Ma's death, and Billie Jo's physical and emotional wounds just that much bleaker. Not convinced? Check out the "What's Up with the Title?" section.