[Mary was] glowering at her daughter[Maggie] in the gloom. Her eyes seemed to burn balefully. "Yeh've gone teh deh devil, Mag Johnson, yehs knows yehs have gone teh deh devil. Yer a disgrace teh yer people, ... An' now, git out an' go ahn wid dat doe-faced jude of yours."
Understanding the quote in relation will be helped by understanding the context of it. Mary is speaking to Maggie. Jimmy is in the room as he just forced Mary in. Pete has just come in and been dismayed at the scene. But previously, in Chapter XIII, the omniscient third person narrator had guided us through Maggie's thoughts about Pete and her life. We first learn that Maggie is quite smitten by--or quite fancies--Pete. He takes her out to pleasant entertainments, like the melodrama plays, where "Maggie always departed with raised spirits from the showing places of the melodrama." She has become self-conscious about her clothing and general appearance, looking with longing at the elegance of "the well-dressed women she met on the avenues." We also learn she laments the effects of her job at the collar and cuff factory will have on her looks, since Pete is particular in his tastes.
She wondered as she regarded some of the grizzled women in the room, ... She speculated how long her youth would endure. She began to see the bloom upon her cheeks as valuable.
Then, the narrator carefully describes the nights out Maggie has with Pete,
Evenings during the week he took her to see plays in which the brain-clutching heroine was rescued ... by the hero with the beautiful sentiments.
and carefully explains the entertainment they go to, complete with the "triumph for the hero." There is a reason for this detailed care: We need to know what Maggie and Pete do when we come to Chapter IX and Mary, Maggie's mother, shouts through her disordered drunken thoughts at Maggie.
The expression, "Yeh've gone teh deh devil," when hurled in that manner at a young woman in the 19th century means that the speaker believes that the girl has been immoral and has failed to defend herself against (or has allowed) the sexual advances of the man she is keeping company with. Therefore when Mary yells this at Maggie, it means she thinks the worst of Maggie and is, in a sense, rejecting Maggie. However, the next chapter reveals that Mary was, as we already know of course, wrong. It further reveals that Pete seems to have taken advantage of Maggie's distress and made Mary's prophecy about going to the devil come true, since Jimmy informs Mary of what he heard from their neighbor. This quote emphasizes the characterization of Mary, Jimmy, and Maggie, revealing something more about each of their characters. It also emphasizes the plot complications and twists that are about to take shape.
Jimmie gave vent to a sardonic curse and then laughed heavily.
"Well, Maggie's gone teh deh devil! Dat's what! See?"
"Eh?" said his mother.
"Maggie's gone teh deh devil! Are yehs deaf?" roared Jimmie, impatiently.
"Deh h--- she has," murmured the mother, astounded.
Jimmie grunted, and then began to stare out at the window.