Mrs. Joe is Pip's much older sister, and oh boy, she is just the worst of every older sister rolled into one: not only does she never let him forget that she "brought him up 'by hand'" (1), she believes in corporal punishment—a lot of it. She even has a favorite torture device called the Tickler, a wax-ended cane.
Like most minor characters, we get a pretty good flavor from her first description:
My sister, Mrs. Joe, with black hair and eyes, had such a prevailing redness of skin that I sometimes used to wonder whether it was possible she washed herself with a nutmeg-grater instead of soap. She was tall and bony, and almost always wore a coarse apron, fastened over her figure behind with two loops, and having a square impregnable bib in front, that was stuck full of pins and needles. She made it a powerful merit in herself, and a strong reproach against Joe, that she wore this apron so much. Though I really see no reason why she should have worn it at all; or why, if she did wear it at all, she should not have taken it off, every day of her life. (3)
Unapproachable, hard, resentful, and prickly—that's Mrs. Joe. We don't know a single thing about her, like why she's so mean (although having to raise her little brother might have something to do with that) or why she even wanted to marry Joe in the first place, but we do know that she's responsible for helping form Pip's character. She makes him "sensitive":
I had known, from the time when I could speak, that my sister, in her capricious and violent coercion, was unjust to me […] Through all my punishments, disgraces, fasts, and vigils, and other penitential performances, I had nursed this assurance; and to my communing so much with it, in a solitary and unprotected way, I in great part refer the fact that I was morally timid and very sensitive. (8.95)
In other words, Mrs. Joe is partly responsible for making Pip so susceptible to Estella's meanness. Maybe if she'd been nicer, making Pip really feel like part of a family and like he was worth something already, Estella's snobby attitude would never have hurt him.