As soon as this short story begins, the grandmother is reminiscing about how things used to be - "back in my day" when children had respect for their elders and when men were "gentlemen." She talks about the man she almost married, a Mr. Teagarden, who brought her watermelons. He was a gentlemen. When the family arrives at Red Sammy's Barbecue, the grandmother shares memories with Red Sammy about how people used to be able to be trusted but that nowadays, "People are certainly not nice like they used to be." Red Sammy shares a story of how he let some men charge gasoline at his station, and the grandmother assures him it is because "You're a good man!" When they talk about the Misfit being loose in the country, Red Sammy says:
A good man is hard to find. Everything is getting terrible. I remember the day you could go off and leave your screen door unlatched. Not no more.
The grandmother prides herself on being able to recognize a good man. Ironically, this gets her and her family killed because she recognizes the Misfit when he and his gang stop on the road after the grandmother and her family have an accident. The Misfit tells her that it is too bad she recognized him:
It would have been better for all of you, lady, if you hadn't of reckernized me
From this point on, the grandmother panics and keeps trying to assure the Misfit that he is a good man, that he comes from good people, that she is certain he is a good man, that he would not shoot an old lady, etc. This is ironic because the Misfit is NOT a good man, and the grandmother's definition of a "good man" has been hollow and meaningless, just like the platitudes she is always saying - "A good man is hard to find," or "Things were better in my day." Many, many of O'Connor's short stories contain these empty platitudes and they show the hypocrisy and emptiness of the people that utter them.
So -- what is a good man? No one knows. This is an empty statement. The grandmother thinks she knows what a good man is, but she does not. She has been so caught up in her selfish desire to visit her childhood home that she has put the family in danger. She has selfishly taken her cat on the trip, which winds up causing the accident. She is a petty woman who utters empty phrases such as "a good man is hard to find."