Fanny is the oldest girl in an impoverished family of many children. Her rich aunt and uncle offer to give her a home with a good education and a proper upbringing. Fanny sleeps in a small room in the attic and mostly acts as a servant, messenger, and companion to her aunts, Mrs. Norris (who is a penny-pincher, an opportunist, and despises Fanny) and Mrs. Bertram (who has her head in the clouds and spends most of her time laying on the sofa with her pug). Fanny has a difficult time because her older cousins, Maria and Julia are blatantly favored over her.
Fanny's cousin, Edmund, is very kind to her and takes time to talk to her and make her feel welcome. Fanny falls in love with Edmund over time, but a wealthy newcomer named Henry Crawford falls for Fanny. Fanny wants nothing to do with Henry. There are a whole bunch of love entanglements in the story but all ends well for Fanny.
I can see two reasons why people say this is their least favorite Jane Austen. One, the story takes a long time to start. You have to read about 1/3 of the book to get all the background and characters established before you can get to the good stuff. People probably lose interest and don't read it all the way through. Two, Fanny and Edmund are goody-two-shoes and nobody can relate to that. They can't even put on a play without feeling guilty and calling off the whole thing. Fanny gets out-of-breath just from taking a simple walk and needs to sit down and rest and be coddled all the time. They are always soliloquizing over moral issues and they can be pretty judgemental at times.
My favorite part of the book is when Fanny returns to her childhood home and is absolutely appalled at the chaos of the home and the brattiness of her siblings. "The boys begging for toasted cheese, her father calling out for his rum and water, and Rebecca never where she ought to be." "The three boys burst into the room together... still kicking each other's shins and hallooing out at sudden starts immediately under their father's eye." Her family offers her tea that never appears because the servant girl always wanders away, her sisters keep fighting over a knife, and there are so many kids in the family that nobody seems to even know who she is or why she is there. Of all Jane Austen's books, this is the only window we get into the life of the poor. The image we get is brilliant - so full of energy and recklessness and hilarity in comparison to the wealthy, stuffy characters her stories mostly focus on.