The Gaang is an unoffical name for the Avatar's group that helps him on his journy to master the Four elements. The group was first formed when Katara and Sokka found Aang trapped in ice at the South Pole. After saving Aang from the Fire Nation, Sokka and Katara travel with him to the North Pole to learn Water Bending.
After travelling basically everywhere, the Gaang arrive in the North Pole. Katara battles Master Pakku after he refuses to teach her because she isn't male, he teaches her after he discovers she's the granddaugter of his former fiance. After the North Pole is destroyed, Master Pakku tells Katara that she is a Waterbending master and is capable of continuing Aang's lessons.
The Gaang venture to the Earth Kingdom to find Aang an Earthbending teacher. Aang did have his mind set on Bumi, but Bumi had been captured by the Fire Nation, and was waiting for his time to strike. They find Aang an Earthbender in Toph, a young blind girl who is able to "see" with her feet, by feeling the vibrations in the ground. Aang learns Earthbending eventually, but has trouble at first because it's the oppisite element of air.
After fighting in Ba Sing Se, Aang is thought to be dead. After a few little adventures in the Fire Nation, the Gaang along with other members of the rebellion attack the Fire Nation. Sadly, Aang isn't able to defeat Fire Lord Ozai during the Day of Black Sun, so all the kids escape on the back of Appa, while the adults surrender. Haru, Teo and the Duke are now members of the Gaang. They currently reside in the Western Air Temple, and Zuko recently joined to be Aang's Firebending teacher. Together they freed Sokka's father Hakoda and girlfriend Suki, from the prison known as "The Boiling rock".