The Misfit is referring to the concept of grace, a state of spiritual favor granted freely by God. In Christian theology, grace is not earned but given as a gift to the unworthy. To be in a state of grace is to be unified with God, which is what happens to the grandmother during the climax of "A Good Man is Hard to Find."
The grandmother is a highly flawed character: she's racist, snobby, dishonest, and thoughtless. When she encounters the Misfit, she initially views him as a bad man, someone lesser than herself. However, the Misfit's emotional breakdown changes something in the grandmother: she suddenly sees him as a broken human being like herself rather than as a criminal beneath her. This is what she means when she calls him "one of my own little babies": she suddenly views him the way God would, as a person in need of love.
After killing the grandmother, the Misfit claims she needed someone to shoot her every moment of her life because she only received this grace-infused clarity when faced with death and pain. Only when separated from her image-conscious, safe little world could the grandmother see clearly and push beyond her snobbish conceptions of other people. Had she never encountered the Misfit, she might never have changed at all. This could be read cynically, but it could also be Flannery O'Connor's way of asserting a universal truth: people often grow when faced with dire situations and tragedy, rarely when life is comfortable.
It's only with the threat of imminent violence that the grandmother has started to show kindness and consideration to another human being. The old lady has spent the whole of her life constantly judging and criticizing others, never once acknowledging that we're all part of the same human family. Yet now, at a moment of crisis, and with a gun pointed straight at her by a crazed, psychotic killer, she reaches out to another human being for the very first time. Now she recognizes that the Misfit is as much a part of the human family as she is, which is why she calls him her son.
But it's all too little, all too late. One cannot, in all conscience, regard the grandmother as a good woman on the strength of one single example of kindness and empathy. If we say that someone is good, it's because they've regularly displayed goodness throughout their whole lives, not in isolated cases like this one.
Ironically, the Misfit, who is far from being a good person himself, instinctively understands this. He knows that the grandmother is one of those people who can only be good when there's some kind of threat hanging over their heads. In other words, she can only be good when forced to be good. And that's not real goodness at all.
As his associate's shooting spree draws to a close, the Misfit hears the grandmother’s dying declarations. Having witnessed her self-centered, foolish behavior, the Misfit understands that this woman was not good. His statement is made partly in reaction to her assertion that he is one of her children. The reader can interpret his reaction in several ways. One way to read this is that he believes her, but not in the way she would like; rather, he understands that they share a quality of evil, not goodness. A different interpretation would be that he does not believe she means they have something in common but thinks she is lying to try to get him on her side. In that case, he would reject her deviousness and hypocrisy. It seems unlikely that he believes she felt a maternal affection for him in recognizing their common humanity.
The Misfit’s assessment of the grandmother’s lack of goodness is associated with the idea of negative reinforcement. He speaks of her as one would of a child, who only behaves properly if they think they will be punished for bad behavior. The grandmother is not a moral being who is capable of right living of her own volition. The fear of death is prompting her to behave in what she thinks is an appropriate fashion, as she appeals to Jesus with her last breaths.
In Flannery O'Connor's world of fiction, grace is often obtained from an act of evil, or through the agency of violence that acts as a catalyst for spiritual epiphany. In the case of the egotistical grandmother who puts her own desires ahead of any of her family members, it is only after her son Bailey and his wife and children are killed and she herself is faced with death that she looks up at the Misfit and recognizes their commonality, "Why....You're one of my own children!"
O'Connor's approach to spirituality is likened to that of the German philosopher Martin Heidegger and his concept of Dasein, "being-there," a state in which death represents the point at which existence becomes complete, whether for better or for worse. Thus, according to critic Elisabeth Piedmont-Marton, when the grandmother repeats, "Jesus, Jesus," she is calling upon her Christian faith, a faith she has merely flaunted rather than lived. Moreover, it is at this point that she truly believes and recognizes her connection to the man who has tried to understand. However, when she reaches out to him with her words that he is like her, the Misfit recoils from her and rejects the grace that he could receive. Nevertheless, the Misfit's final words about her--"if it had been somebody there to shoot her every minute of her life"--acknowledge his role in the grandmother's attainment of grace.