Mrs. Pegler is Mr. Bounderby's mother who took as much care of her son as the most loving mothers of the world ever did. Mr. Bounderby, who wishes to perpetuate the story that he is an entirely self-made man, tells her never to contact him in public and goes around telling everyone that his mother deserted him at a young age to his drunken grandmother (he never had a drunken grandmother, either). She spends most of the book as a mysterious old woman who hangs around Mr. Bounderby's factory from time to time, inquiring after his well-being, but her true identity is accidentally revealed by Mrs. Sparsit at the end of the book.
The timeline below shows where the character Mrs. Pegler appears in Hard Times. The colored dots and icons indicate which themes are associated with that appearance.
Book 2, Chapter 6
...old woman he met the last time he was at Bounderby's house, whose name is Mrs. Pegler . Stephen and Rachael politely make conversation with the mysterious old woman, who again makes... (full context)
Book 3, Chapter 4
Book 3, Chapter 5