Mrs. Jones treats Roger kindly because she understands what he is going through.
Roger tries to steal Mrs. Jones’s purse, but instead of trying to call the police on him, she takes him home and makes him something to eat. She is nice to him, because she realizes that he is just a sad boy with no one to look after him and nowhere to go, and she has been where he’s been.
Mrs. Jones seems aware when she looks at Roger that he has no one at home.
"Um-hum! And your face is dirty. I got a great mind to wash your face for you. Ain’t you got nobody home to tell you to wash your face?"
"No’m," said the boy.
Once she has him home, she treats him very kindly. It is clear that she has empathy for him. She probably grew up under similar circumstances, not having anyone at home.
When the conversation comes around to why Roger stole, Mrs. Jones shares her situation and it is clear that she empathizes with Roger wanting something he did not have.
The woman was sitting on the day-bed. After a while she said, "I were young once and I wanted things I could not get."
… I have done things, too, which I would not tell you, son—neither tell God, if he didn’t already know…”
By the end of the conversation, Mrs. Jones has Roger’s trust, and he wants her to trust him. He feels badly about what he has done, especially since she says he should have just asked for money, and he even asks her if she wants him to go to the store. He clearly appreciates the mothering she is doing, telling him to wash his face and offering him food, and he also appreciates her opening up to him.
Mrs. Jones seems to live alone, and she does not have any children. Based on this example, she would be a good mother. She is tough but firm, and she teaches Roger a good lesson about forgiveness and need. She does not judge him, but instead takes care of him for an evening--which he needs more than new shoes.