After the verdict is read, and Tom is found guilty, the black community, sitting in the balcony of the courthouse in their segregated section, rises as a whole when Atticus walks out of the courthouse. They know that Atticus has done his best to defend Tom Robinson.

After the trial, food is brought to Atticus’s home as a sign of respect and thanks. Atticus is embarrassed by the amount of food he receives because he knows that the blacks are poor and that it is probably a hardship for them. Remember, the story takes place during the Great Depression, and it is probably the only means they they have for thanking Atticus.

The black community shows respect for Atticus several times throughout the story. Before Tom Robinson’s guilty verdict, they welcome Scout and Jem into their church when Calpurnia brings them to a service. Although there is a little dissention from a couple of worshippers, Reverend Sykes quiets the complaining and embraces Scout's and Jem’s attendance. 

It’s interesting to note that there are two places in the novel where food is given to Atticus to pay off a debt or to show respect. At the beginning of the novel, Walter Cunningham, Sr., brings Atticus hickory nuts and firewood to pay for legal services; later, after the trial, the black community brings Atticus baskets of food that show gratitude for his kind endeavors to prove Tom Robinson innocent.

In Chapter 22, Tom's father sends a chicken over to Atticus on the morning after the trial. Calpurnia cooks it, and Atticus remarks that they don't even eat chicken for breakfast in the White House. Cal then informs him that Estelle from the hotel sent over rolls, too. When Atticus looks surprised, she shows him the kitchen table, which is loaded with "hunks of salt pork, tomatoes, beans, even scuppernongs," pickled pigs' knuckles, with more food gifts on the back steps. Calpurnia explains for Atticus:

"They—they 'preciate what you did, Mr. Finch. They—they aren't oversteppin' themselves, are they?" (213).

Atticus tears up and says that he is grateful but that they shouldn't do that again because there's a depression going on in the country, and the black community has it harder than anyone else. 

Tom's family and friends were like most everyone else during the Great Depression. They may have had some food that they grew or harvested on their own, but few--and none in their local community--had money to pay for legal services. Atticus never asked for payment, but, as Cal said, the community appreciated the honest effort he put forth for Tom's sake and wanted to show him this appreciation in the best way they knew how.

The black people of Maycomb shower Atticus with gifts of food to show their appreciation for his act of defending Tom at the trial. They do this almost as soon as the trial has ended. Atticus is amazed when he sees all the food piled up: 'enough food to bury the family', as Scout observes in a hometown allusion to food being given after a person's death (in itself, foreshadowing of Tom's ultimate fate).

Atticus's reaction to these gifts is telling. At first he appears amused when he 'grins' at seeing a 'jar of pig's knuckles' and wonders: 'Reckon Aunty'll let me eat these in the dining room?' However, just a moment later the tone changes when we are told that his 'eyes had filled with tears'. He is overcome at the generosity of these people and at the fact that they appreciate him as their champion.

The incident also paints a perhaps rather-too-good picture of the blacks as being humble and thankful as a whole community. As Atticus remarks: 'times are too hard', meaning that there is an economic depression on and that, thanks to the deplorable racist conditions of society, the blacks are poorer than anyone else in the town. Yet, Lee suggests they still give their food unstintingly as a whole community to Atticus in the nature of a grateful offering.

Incidentally, this is the only time that Atticus is ever seen to cry in the novel. This shows how just deeply he is touched by these gifts of food and gestures of thanks. 

After the trial, the black community shows its thanks by bringing all kinds of food for Atticus and his family.  Tom Robinson's father gives a chicken and other people leave all sorts of stuff on the back steps.

The reason they are doing this is that they are grateful to Atticus for standing up for Tom Robinson.  They believe that he has done all he could to keep Tom from being convicted.  So they are expressing their thanks for Atticus's treating Tom like a real person and for trying his best to get him off.