Toph Beifong is by far one of the most interesting characters in Avatar: The Last Airbender. Despite making her first appearance in the second season, The Book of Earth, she feels like she was always part of the world of Avatar.
The Blind Bandit is famed for her exploits as much as her attitude. But as cool as Toph is, her family is actually cooler--and an even more important part of the world. The Beifongs have influenced the Earth Kingdom for centuries.
10 Beifong's Meaning
The name Beifong means "Northern Territory." This is ironic, as the family do not live in the north at all, but rather have historically resided in Gaoling, a city in the southern part of the Earth Kingdom.
Nerdwire's excellent YouTube video on the Beifong family has observed that the name is a reference to their high position in the Earth Kingdom's social structure that comes from their immense wealth, rather than having anything to do with their physical place within the geographical layout of the Kingdom.
9 Toph's Name
There are three theories on the meaning of Toph's name, but the truth is actually uncertain, which is itself quite telling, since Toph has never been one to let others define her.
The most obvious meaning of her name is the English word "tough," which definitely suits her. After all, it is hard to think of a tougher character. However, there is also the UK slang word, "toff," denoting someone of wealth and privilege in society--a description which applies to all the Beifongs. Beyond either of these explanations, her name also means "Expanding Lotus" when translated from Chinese--which sounds beautiful, but does not seem in keeping with her character.
8 When Pigs Fly
The sigil of the Beifongs is a Flying Boar, an animal which evokes the English saying "when pigs fly," denoting an incredibly unlikely event--something also noted by Nerdwire in their video on the family. Toph and others in the family repeatedly achieve the impossible, whether it is inventing metalbending, overcoming powerful enemies, or reinventing industry.
There is at least one example of an actual Flying Boar in Avatar, but there is a far more interesting example within the family. In The Legend of Korra, one of the younger Beifong family members, Opal, really does learn to fly when she becomes an Airbender.
7 Rarity of Surnames
There are not a lot of characters who have a last name in the world of Avatar. In fact, the Beifongs are the only characters with canonical surnames in the entire run of Avatar: The Last Airbender.
It seems surnames are distinct to the nobility. This might explain why both Sokka and Aang hilariously fail to invent plausible last names when they create false identities for themselves. The only other surname in either Avatar show is The Legend of Korra's Sato family.
6 Working with Firebenders
Toph's father, Lao Beifong, was the first person from the Earth Kingdom to form a business with someone from the Fire Nation, creating the Earthen Fire Refinery.
This refinery helped with the technological developments that led to The Legend of Korra's steampunk aesthetic, combining the combustion technology of the Fire Nation with the Earth Kingdom's metallurgical mastery.
5 Metalbending
The Beifongs invented metalbending. Well, technically speaking, Toph invented it, but her family helped develop it as a formal discipline with different industries and techniques.
Toph's daughter Suyin founded the city-state Zaofu, home of the Metal Clan. She also married Baatar, a skilled architect who helped design the city. Their twin sons Wing and Wei took this a step further when they invented a metalbending sport called power disc.
4 The Family Home
The ancestral home of the Beifongs in the city of Gaoling was based on a traditional Chinese structure, the siheyuan. Temples and palaces were commonly built in the siheyuan style.
In real life, these buildings have been in use in China for roughly two thousand years, so it makes sense that the Beifongs ancestral home would be a siheyuan. This also suggests that the family have been wealthy and powerful for a very long time, and that they have deep roots in the southern Gaoling area, despite their name meaning "northern territory."
3 Police
A number of the Beifong family have become police officers. While Toph was a police chief for a while, her daughter replaced her as a member of law enforcement.
Considering that Toph was born to parents whose job was basically just to be rich influential aristocrats, taking this hands on approach to confronting potential threats is something that it is hard to imagine most of Toph's ancestors doing, despite it eventually becoming a tradition among women of the family. Other members of the Beifong family gravitated toward the world of industry.
2 Connection to the Avatar
At least four different versions of the Avatar have had ties to the Beifong family, though just how close the connection was varied.
The Avatar Kuruk's Earthbending teacher was close friends with Lu Beifong, who searched for the new incarnation of the Avatar, Kyoshi. Toph obviously was close to the Avatar Aang, affectionately calling him "twinkletoes," while Aang's successor, Korra, became allied with a number of the Beifong family members.
1 Alternate Toph
Originally, Toph was never going to be part of the series. Instead, a tall musclebound jockish guy was supposed to be Aang's Earthbending teacher.
Originally, Toph was conceived of as a joke by the creative team working on Avatar. The idea of a little girl who would be the toughest character of the group was something the storytelling team thought was hilarious. Thankfully, Toph's character grew over time until she became the character that fans know and love. The rest is history.