Scare quotes (also called shudder quotes, sneer quotes, and quibble marks) are quotation marks a writer places around a word or phrase to signal that they are using it in a non-standard, ironic, or otherwise special sense. Scare quotes may indicate that the author is using someone else's term, similar to preceding a phrase with the expression "so-called"; they may imply skepticism or disagreement, belief that the words are misused, or that the writer intends a meaning opposite to the words enclosed in quotes.
Writers use scare quotes for a variety of reasons. They can imply doubt or ambiguity in words or ideas within the marks, or even outright contempt. They can indicate that a writer is purposely misusing a word or phrase or that the writer is unpersuaded by the text in quotes, and they can help the writer deny responsibility for the quote. In general, they express distance between writer and quote.
As you can see, there is no single interpretation of the meaning. Generally speaking, they are synonymous with the air quotes that people make while saying a word in actual conversation.
If I had to guess at the meaning of the quotes in this sentence (more context might make it more obvious), I would say that the scare quotes are assigning a kind of patronizing disdain to those who express skepticism.
When I read the sentence on its own, I think of something like the following:
"Now, now. A real bogeyman would have killed you by now. So, I'm sure you have nothing to worry about."
→ Her father wasn't helpful. He kept talking about "real" bogeymen.
"You know, real men don't eat quiche."
→ Men got tired of hearing that "real" men don't eat quiche.
I am, of course, assuming an emotional intent behind the word in your sentence that may or may not exist. Based on context, it's possible that the surrounding text actually is talking about diagnosing some things as real and other things as imaginary—there may even have been an earlier quotation, in which the word real was used. In that case, the quotation marks wouldn't be scare quotes but literal quotation marks without any kind of emotional content.
In short, it's open to interpretation what intent the author had with that sentence. But since quotation marks were put around the word real, it's obvious that it's being singled out for some kind of reason.