"Women are available in all shapes and sizes and many are willing to sell their souls, not to mention their bodies, for the slightest bit of financial stability" in the sentence mentioned above, it means "moreover". then i looked up for its synonyms, which is "let alone". its example is given below: "she can't boil potatoes, let alone cook a meal". What's the drill? i'm getting confused now
It's a common English idiom. "X, not to mention Y" means that X is true, and Y is also true but is less important. Often, the idea is that if big thing X is true, than smaller thing Y logically follows. The idea is that if X is true, it's almost not worth even saying that Y is true, because it's obvious or not important. Of course the writer must think it is worth mentioning, because he did mention it. That's why it's an idiom and not a literal statement. It can be positive or negative.
"By marrying the rich man's daughter, I got a beautiful wife, not to mention a great job." The important thing is that I got the girl, but there was also the side benefit of getting a good job.
"The fire at the factory cost us millions of dollars in repair costs, not to mention the lost sales." The big issue was that we had to spend a lot of money to fix the factory. In addition, presumably because the factory is not producing products to sell, we also lost potential sales.
In your example, selling her soul is a bigger issue than selling her body.
Note that you could also say "not to mention" literally, meaning that something should not be talked about. Like, "When you meet Mr Jones, try not to mention that he's bald -- he's very sensitive about this." This is a very different meaning from the idiom.
I forgot to mention "let alone"!
Yes, "let alone" means essentially the same thing as "not to mention". I think "let alone" is only used with negatives. You can say, "I hate vegetables like beets, not to mention asparagus", or "I hate vegetables like beets, let alone asparagus". Those are equivalent. But I can't think of an occasion where you'd it for a positive: "I love desserts like ice cream and cake, not to mention cherry pie." I don't think you'd say, "I love desserts like ice cream and cake, let alone cherry pie."
I don't know the origin of the phrase. Maybe, possibly, the idea is, "I don't want to even touch that thing: leave it alone." But I'm just guessing.