Hermione is a young girl. Her family are "muggles", which means that they don't have any magical powers. Nevertheless, they have great pride in their daughter's abilities.
She is sometimes bullied by cruel pupils who claim that she isn't naturally gifted, but she always proves them wrong with her impressive mastery of spells.
She is probably the brightest student at Hogwarts. She can often be found at the library, her nose buried in books.
The first time she meets Harry, and Ron, she mocks Ron for his inability to perform a spell to turn his rat yellow. She proves just how much she knows by declaring that she memorized all the textbooks by heart. She constantly annoys her peers with her knowledge, so Harry and Ron initially consider her arrogant, especially after she criticises Ron's incantation of the Levitation Charm. She is a little know-it-all and can sometimes be seen as a bit arrogant because of her encyclopaedic knowledge, but she would do anything for her friends and often comes out with the solution to help Harry. Although she dislikes breaking school rules, she lies to protect Harry and Ron from punishment and thus wins their friendship.
Hermione is the brain behind the plan to enter the place where the stone is hidden.