Chapter 2 of The Scarlet Letter, titled "The Marketplace" explains, among other things, the purpose and goal of the scaffold. According to the narrator, the use of the scaffold was to promote good citizenship. It instilled the same horror as "the guillotine" did with the "terrorists in France". The goal of it was to prevent the culprit from "hiding their shame" and to make the accused stand in front of the crowd, admitting to the fact that a transgression has been committed.
The very ideal of ignominy was... made manifest in this contrivance of wood and iron. There can be no outrage... more flagrant than to forbid the culprit to hide his face for shame; as it was the essence of this punishment to do.
Hester's particular punishment was to stand at the scaffold for a period of time and render herself susceptible to any comment, sneer, or criticism coming from the crowd that looks at her. She is holding her child at this time, making the magnitude of her indiscretion even more evident. However, Hester is at all times defiant. She is defiant when her guard removes her from her cell, and she is also defiant when the crowd begins to sneer at her. The importance of this exchange of glances is that Hester is quite aware that her village is a mere settlement of people who follow each other sheepishly and without questioning a thing.
Of an impulsive and passionate nature, she had fortified herself to encounter the stings and venomous stabs of public contumely, wreaking itself in every variety of insult
Hester is aware of the ignorance and hypocrisy that permeates the settlement. She knows that Dimmesdale is weak and that he fell into temptation even though he is the most respected elder in the village. She knows that Mistress Hibbins, Governor Bellingham's own sister is a witch who is allowed to practice her beliefs without being punished; that the entire leadership of the town is as prone to corruption as she was. Therefore, Hester looking down at them is a symbol of how, in the end, they are just as sinful as she is. However, the fact that she stands at "a shoulder's height" above them is allegorical to Hester STILL being at a higher spiritual and intellectual level than all of them. This is because, even though Hester committed a sin, she is aware of her actions and does not sell herself to religion like the rest of the villagers; she is what we could consider a modern thinker in that respect. Hence, to have an entire town of ignorants looking up at a person, and to have that person look down on them is a symbol of Hester's natural higher rank than theirs.