Toph is an in-your-face, snarky 12-year old, and a master Earthbender. She was born blind, but can "see" with her feet by feeling the vibrations on the ground.
She is the only daughter of the Bei Fong family, who are extremely wealthy. However, her parents believed her to be fragile, tiny, and helpless, so they hid her from the world. Most of the people in town did not even know she existed, except for Master Yu the local Earthbending teacher. Toph had private lessons for years where she was only taught basic Earthbending forms and breathing exercises. But Toph was stronger than that and trained on her own.
In secret she went into town and joined the Earth Rumble 6, an Earthbending wrestling tournament, under the name The Blind Bandit. She's done extremely well, and eventually became the undefeated champion. Her record stands at 42 wins and 1 loss -- that loss being from Aang, who used airbending to win. She later repaid him back.
Toph's fighting style is different from most Earthbenders because where they use forms based on the Hung Gar martial arts, Toph uses the Southern Praying Mantis style. She is also an expert at neutral jing -- waiting and listening before attacking -- and often uses the opponent's momentum against them.
When Aang found Toph he asked her to be his Earthbending teacher, convinced it was meant to be because of a vision he had while in a mystical Swamp. Toph was against the idea at first because of the circumstances in her life. But after her secret life was revealed to her parents due to being kidnapped by the Earth Rumble 6 group (where she proceeded to kick their butts), her parents ordered that she be guarded 24/7. Aang became her only route to freedom, and she took it. Her father convinced that the Avatar kidnapped Toph, offered Master Yu and Xin Fu (leader of Earth Rumble 6) a chest full of gold pieces to bring his daughter home.
Toph now travels with Aang, Katara, and Sokka on Appa, and is teaching Aang earthbending. Her teaching style is rough and direct like a drill sergeant, which is good since Earthbending is very straightforward. (Though it does take Aang some time to get use to it). Her social skills aren't that great though at first, and she and Katara get into a couple of "conflicts". Determined to show that she can take care of herself, she doesn't help out much around camp and barely accepts help from others. However, a chat with Iroh helps her see a different perspective on the matter, which brings more harmony to the group.