To answer this question, we first need to discuss what made Matilda's life intolerable: her parents. Despite showing signs of brilliance from her infancy, Matilda is ignored and maligned by her parents. When the child prodigy asks for a book to read—at age four—she is told to go and watch "the telly." In a nutshell, she is a neglected child who has no positive role model in her life.
The first thing that makes her life more tolerable is her decision to take revenge against her parents in whatever ways she can. For starters, she applies superglue to the rim of her father's hat, and it gets stuck to his head. Later, after he rips up the book she is reading, she borrows a parrot from her friend, shoves the cage up the dining room chimney, and manages to convince her family that the room is haunted.
I would argue that the thing that really made a difference in Matilda's life, however, is meeting Miss Honey, her teacher at school. Miss Honey is immediately convinced that Matilda is the smartest girl she has ever met and resolves to help her learn as much as possible. She also soon learns the truth about what Matilda's parents are like. Miss Honey is witness to the moment when Matilda discovers that she can move things with her mind, and this strengthens her desire to help the little girl. Having Miss Honey in her life makes life infinitely more tolerable for Matilda.
In time, Matilda learns of Miss Honey's troubles with the school headmistress, Miss Trunchbull, and takes action to set things right for her favorite teacher. In the end, Matilda's life is made not just tolerable but happy when she goes to live with Miss Honey.