The “abysmal life-giving knowledge” is that Mrs. Turpin has a sobering and deep revelation about how she has been living her life.
The word abysmal has a double meaning. It can mean depressing, but it can also mean deep like looking into an abyss.
A red glow suffused them. They appeared to pant with a secret life. Until the sun slipped finally behind the tree line, Mrs. Turpin remained there with her gaze bent to them as if she were absorbing some abysmal life-giving knowledge.
Mrs. Turpin has been accustomed to thinking of herself as better than everyone else. She always knows more than everyone else. She thinks of herself first. It never occurs to her that she may not be the be-all-and-end-all. When she meets the fat girl in the doctor’s office, her life is changed. She gets a wake-up call in the form of a book thrown at her head and some cutting remarks.
When the girl throws the book, Mrs. Turpin has an almost religious experience. She” held her breath, waiting, as for a revelation. “It is as if she knows that what the girl is about to say to her is important.
"Go back to hell where you came from, you old wart hog," she whispered.
At this point, the girl smiles because the message has “ struck its target” and reached Mrs. Turpin.
Apparently it did. The book was on human development. Mrs. Turpin develops and grows as a result of the experience. She seems to see the world as if for the first time, and realizes that she is going to go to Heaven now, even if she was not about to before.
The double meaning of the word “abysmal” is a clever way to add ambiguity to the story. It could be interpreted as either meaning, or both meanings at the same time. She might have been depressed by it, or she might have been enlightened by it. Which one depends on whether you are pessimistic or optimistic about human nature.