In chapter 12 of To Kill a Mockingbird, what is the purpose of the Sunday collection at Calpurnia's church?

In Chapter 12, Scout and Jem visit First Purchase African M.E. Church for Sunday service with Calpurnia. Following the sermon, Reverend Sykes requests the morning offering, and the congregation put their coins into a coffee can. Interestingly, Reverend Sykes empties the can and counts the coins. He then tells the congregation that there is not enough money and that they must collect ten dollars. Reverend Sykes then mentions that the collection is for Helen Robinson and her children. Afterward, Scout asks Reverend Sykes why the congregation was donating money to Helen and her family. Reverend Sykes explains to Scout that Helen is having difficulty finding a job and the congregation must help her out any way they can. Nobody in Maycomb is willing to offer Helen Robinson a job because of the crime her husband is accused of committing. However, Reverend Sykes does mention that Link Deas might offer Helen a job. 

The collection at Calpurnia's church where she takes Jem and Scout is for Helen, the wife of Tom Robinson.  That these poor members of a church without even hymn books would take up a collection for another of their community is in sharp contrast to Aunt Alexandra's Missionary Society in the very next chapter that sends money overseas to remote Africa not knowing whether the "charity" gets to anyone anyway. Also, it points out the hypocrisy of the ladies who "charitably" give to Africans, but are unconcerned about their neighbors who suffer. This action of the members of Calpurnia's church underscores the meaning of the aphorism that "true charity starts at home."

What is the purpose of the Sunday's collection at First Purchase Church in To Kill a Mockingbird?

The purpose of the collection is to aid Tom Robinson's wife while he's in jail.

When Mayella Ewell accuses Tom Robinson of rape and he's put in jail, it makes things difficult for Helen and their children. Without Tom, the household doesn't have as many resources.

Calpurnia takes Jem and Scout to First Purchase African M.E. Church with her one Sunday morning where they attend church services. When Reverend Sykes is making announcements, he says:

"You all know of Brother Tom Robinson’s trouble. He has been a faithful member of First Purchase since he was a boy. The collection taken up today and for the next three Sundays will go to Helen—his wife, to help her out at home."

When the collection is gathered in the black enameled coffee can, Reverend Sykes says it isn't enough. He reminds everyone that Helen can't leave her children to work and says they have to make at least ten dollars. He instructs someone to shut the doors and says that no one can leave until they've reached that amount.

When Scout is leaving, she asks Reverend Sykes why Helen can't take her children to work with her when so many other women do. He says that Helen is having trouble finding work. Calpurnia tells Scout that because of the crimes of which Tom's accused, people are not associating with the Robinson family. 

Calpurnia decides to take Jem and Scout to the First Purchase AME Church because Atticus was out of town, and he had not given Cal any specific instructions about going to church. Cal was worried that if she allowed the children to go alone, they would get in trouble again, just as they had when they tied Eunice Ann Simpson to a chair in the furnace room. So, Cal made sure the kids were spruced up, and she took them to her church. On this Sunday, Reverend Sykes announced to the congregation that

"The collection taken up today and for the next three Sundays will go to Helen--(Tom Robinson's) wife, to help her out at home."