We don't get to learn much about George and Harry's mother except that she's one of the people who prays for George on the night of his crisis. Her finest moment is when she helps George realize that Mary Hatch is in love with him:
MA BAILEY: Can you give me one good reason why you shouldn't call on Mary?
GEORGE: Sure—Sam Wainwright.
MA BAILEY: Hmm?
GEORGE: Yes. Sam's crazy about Mary.
MA BAILEY: Well, she's not crazy about him.
GEORGE: Well, how do you know? Did she discuss it with you?
MA BAILEY: No.
GEORGE: Well, then, how do you know?
MA BAILEY: Well, I've got eyes, haven't I? Why, she lights up like a firefly whenever you're around. [...] And besides, Sam Wainwright's away in New York, and you're here in Bedford Falls.
Sly one, that Ma.
When Clarence is giving George his life tour, we see what would have happened to Mrs. Bailey if George had never been born. It's not pretty. Grieving the loss of her son (who died since George wasn't around to rescue him) and husband, she's a bitter, sad woman running a boarding house. Thanks to George, her life is totally different.