Kurt Vonnegut once wrote a list of 8 rules for writing short stories. He ended the list by saying that Flannery O'Connor broke all of them except the first ("Use the time of a total stranger in such a way that he or she will not feel the time was wasted.").
He clearly meant this as a compliment, and he was right on. How she wrote the stories in this collection and made them as good as they are just doesn't add up. Another rule on Vonnegut's list is to "give the reader at least one character he or she can root for," and it is the one she most consistently breaks. The characters with whom one identifies (other than a child or two) are usually just the least despicable.
All the same, Vonnegut was right to say that she never breaks the first rule. Every story in this collection is stunning, haunting, and impossible to ignore. The title story might be one of my favorites ever. In fact, The River might be another.
One thing O'Connor does is introduce you to a character who is ruminating on his or her (usually her) annoyance with another character, suggesting to the reader that the object of the rumination likely has a deeper, more justified, and more profound resentment or even hatred for the one ruminating. This is an interesting motif, but it hardly accounts for the excellence of these stories in the face of such unlikable characters. But the excellence is undeniable.
So then: what is it that makes these stories so great? Honestly, I couldn't say.