While I agree with the previous Educator's analysis, I'll offer the additional possibility of reading Aner Clute as a kept woman—that is, a woman who attaches herself to wealthy men and offers them her company. One could argue that this is still a form of prostitution, though more selective, because there's still an exchange of sex and money.
Aner leads an itinerant lifestyle, but what remains the same in each place is the curiosity about how she became a woman who lives off of men:
OVER and over they used to ask me,
While buying the wine or the beer,
In Peoria first, and later in Chicago,
Denver, Frisco, New York, wherever I lived,
How I happened to lead the life,
And what was the start of it.
What is interesting is that Aner Clute responds in the way that men expect:
Well, I told them a silk dress,
And a promise of marriage from a rich man—
(It was Lucius Atherton).
However, her real reason for becoming a prostitute, or a kept woman, is related to everyone's insistence on characterizing her in a particular way due to choices she makes. Instead of rejecting the story that people started to tell in her town, that she is a woman who will exchange sex for money or nice things, she continues to tell the story, allowing for it to be the narrative that determines who she is. Her analogy of the boy who steals the apple suggests that, once she got a particular reputation, it became difficult for her to make other choices in life. Aner doesn't blame herself but her town for judging her according to a single act.
The story of Lucius Atherton follows hers. In reading it, we learn that he was a "rural Don Juan" who may or may not have been rich. The only indication that we have of any wealth is a diamond stud that he wore, which may have been a gift from another one of his women. Lucius ends up poor, loses his looks, and realizes that he has never loved anyone.
In Line 5 of "Aner Clute" from Spoon River Anthology, Aner discusses how no matter where she goes, people ask her how she ended up leading the life (becoming a prostitute). Aner tells her "interrogators" that she was once promised a "silk dress" and marriage, and those false promises led to her occupation. However, Aner then uses an analogy of a boy being accused of stealing to explain that when someone is accused repeatedly of being something, that person ends up living out those expectations (the boy becomes a thief in Aner's analogy; Aner becomes a prostitute seemingly because of others' low view of her). The last two lines of the poem claim that
It's the way the people regard the theft of the apple
That makes the boy what he is.
Aner, as the speaker of the poem, seems to be directing her comments to people from her hometown, almost as if she is warning them to be careful of how they craft others' reputations.