I grew up in Atlanta and you could see it in quite a number of places around town, thought it's a very subtle thing. You'd be driving past an apartment complex in a poorer neighborhood. At first it doesn't look any different but look closer at the stores around that neighborhood.
It's usually going to be a mix of gas stations, fast food joints, dollar stores and maybe a Kroger (forget Walmart or Publix, they only serve the nicer parts of town with a few exceptions). Other than the Kroger, there's really no other options for fresh food, and if you live >1 mile from the Kroger then it's going to be challenge to walk there.
Often times a food desert seems hidden to someone in a car, you drive along and see some gas stations then down the road you see a Kroger or another grocery store. While to you in a car it's just "the store is down the street", to someone walking the store might as well not be there.
And the problem with fixing food deserts is that fresh produce is much lower margin than other items in the store. A full sized grocery store can handle that and keep produce as a loss leader but a place like Dollar General simply cannot afford to keep produce on the shelf unless they price it higher in which case it becomes unaffordable for the people that need it most.