in the town. And as Aunt Alexandra knows, they often have illustrious roots in the past.

Below them are the deserving poor, such as the Cunninghams. These are people who do without—for example, the Cunninghams can't afford to bring lunches to school—but have pride. They work hard, don't take take handouts, and pay their debts however they can, even if it is through barter.

Next are the white trash, like the Ewells. They are considered lazy and are looked down upon because they don't work hard and instead accept charity. The Ewell children don't go to school. Bob Ewell is an alcoholic, which makes him a blot on the community. Families like the Ewells are isolated and ostracized.

Black people rank below even white trash in the Maycomb social hierarchy. White supremacy is upheld at all costs, and even the most honorable and hardworking Black people are expected to kowtow to lower-class white people. The word of white person is always accepted over the word of a Black person.

Jem explains the social hierarchy of Maycomb to Scout in Chapter 23 of To Kill a Mockingbird. After Aunt Alexandra firmly informs Scout that she cannot bring Walter Cunningham home after school to stay the night because the boy is "trash," Scout is deeply disturbed. Jem tries to explain the situation to her:

Jem elaborates that one kind of people also dislikes another kind of people; for example, people from Atticus' family don't respect the Cunninghams due to their lack of interest in education and the fact that they are "yappy" folks who "like fiddlin' and things like that." In turn, the Cunninghams despise the Ewells for their dependence on government assistance and refusal to live off the land or do hard work. The Ewells hate the black people of Maycomb, discriminating against them only because of the color of their skin. This system, although deeply prejudiced and unfair, has become an integral part of maintaining the socioeconomic status quo of this little Southern town. 

This is a good question. There is no one place where a hierarchy is given. However, if we piece things together we can come to a few educated conclusions. 

First, Atticus and his family are pretty high up on the social hierarchy. Scout on several occasions talks about their family's heritage in Maycomb. Also Atticus is a lawyer and Jack, his brother, is a doctor. Also Alexandra is akin to a socialite. 

Second, there are others in the town like Heck Tate and Ms. Maudie. They are the average citizens of the town. They are white and solidly middle class. 

Third, you also have poorer citizens, like the Cunninghams. We know that they are poor because Walter did not have food or money for food at school. Scout says that they just get by. Also Walter's father does not pay Atticus for his legal services in money but in nuts and other food stuff. 

Below the Cunninghams you have the really poor - Bob Ewell and his family. The town lets them do whatever they want, like hunt off season, because they feel sorry for him. 

Finally, you have the blacks. They are generally taken advantage of. This is why Tom was accused of a crime, even though he was innocent. 

Maycomb’s social hierarchy is very distinct and easy to determine. At the top of the social ladder are the educated, land-owning whites, like Atticus Finch. In a small town in the Deep South, owning land gives a person or family prestige and respect. The next step down on the social ladder would be the hard-working whites, the farmers, like Walter Cunningham.  Here it is obvious that hard work is what is rewarded, not the amount of money one had. Walter Cunningham has very little money but works hard to maintain his dignity and will not take charity from anyone. The next step down the social ladder is the non-working whites like the Ewells. The last and lowest rung of the social ladder is where all the African-Americans in Maycomb were. No matter the education, wealth, or land-owning status, this was their place in society. It is this discrepancy and disgrace that Harper Lee highlights in the novel. She questions a society where someone like Bob Ewell could rank higher in society than Calpurnia or Tom Robinson.  

Jem tells Scout that there are “four kinds of folks” in Maycomb based on class and race.

The trial’s outcome came as a bit of a shock to Jem.  He was expecting a verdict of “not guilty,” because he believed that Atticus proved Tom Robinson innocent.  When Aunt Alexandra tells Scout that Walter Cunningham is “trash,” Scout is offended.  Jem tells her he understands. 

“… I’ve got it all figured out, now. I’ve thought about it a lot lately and I’ve got it figured out. There’s four kinds of folks in the world. There’s the ordinary kind like us and the neighbors, there’s the kind like the Cunninghams out in the woods, the kind like the Ewells down at the dump, and the Negroes.” (Ch. 23)

To Jem, this social hierarchy is based on who can look down on whom.  The Cunninhams may not have much, but they are better than the Ewells. All the Ewells have is being able to look down on people like the Robinsons, who because of the color of their skin are considered inferior in Maycomb.

Scout is puzzled by the concept that the Finches are superior.  It is important to Aunt Alexandra.  It is not important to Atticus, but he tried to explain it to Scout and Jem to appease her.  She asks why the Cunninhams are not “Old Family” then.  Jem tells her they don’t count. 

“Background doesn’t mean Old Family,” said Jem. “I think it’s how long your family’s been readin‘ and writin’. Scout, I’ve studied this real hard and that’s the only reason I can think of. Somewhere along when the Finches were in Egypt one of ‘em must have learned a hieroglyphic or two and he taught his boy.” (Ch. 23)

The fact that the Finches are from an important family is meaningful to them because, as Jem says, it is all they have.   They do not have a fortune to go with the family name.  They may be respected, but all they have is respect.  They no longer have the power and money to go with the name.

In chapter 23, page 230, Jem tells Scout that "there's four kinds of folks in the world." The first type are normal people like themselves who are relatively well off; the second are poor farmers like the Cunninghams who can only pay for things through trading their goods; the third are poor unemployed white people like the Ewells who have no ambition and live on welfare; and the fourth are the whole of the black population who find it difficult to get along simply because of their race.

Each kind has despised each other for so long that they can probably never improve their situation. They are forever stuck with their own kind. Jem says that even if their family currently only has as much money as the Cunninghams, because of their family roots, they are still above them in the social order.

At the end of his speech, interspersed with protests from Scout, he says that he thinks that this social hierarchy is the main reason that Book Radley stays indoors. He just doesn't want to face such a hateful world.

The quote to which you are referring:

You know something, Scout? I've got it all figured out, now. I've thought about it a lot lately and I've got it figured out. There's four kinds of folks in the world. There's the ordinary kind like us and the neighbors, there's the kind like the Cunninghams out in the woods, the kind like the Ewells down at the dump, and the Negroes.

This shows his immaturity, naturally, because he thinks he is superior. As a young adolescent, he is just trying to figure things out for himself, and he has become aware of prejudice all around him. He also realizes that the Ewells are part of the lower hierarchy of society.

If you read Scout's response, you will see that she actually has a more mature grasp of life.

The small town of Maycomb is a microcosm of society in general, with a definite stratification, so to speak, of the population. The idea of social position was very strong in the South during the 30s, almost approaching in dogma the caste system seen in some Eastern cultures today.

The Great Depression, however, "smudged" the permimeters separating the classes, and as seen in the story, trading services in the place of money was a common practice. The court case in question bridged across all social levels as Atticus Finch, a reputed lawyer from an established family, defended Tom Robinson, a poor Negro.

Check out the reference below, an excellent essay treating in depth this subject.