Jeong Jeong is a strong, enlightened man who has seen more than his share of the cruel reality of war. Once an honored Admiral of the Fire Nation military, he left and became known as The Deserter. Because he was the first person to abandon his military and survive, he's considered a legend.
He lives in the Earth Kingdom wilderness to avoid Fire Nation soldiers and bounty hunters, and travels with a small group of followers including Chey, the second man to survive leaving the Fire Nation army (and quite the JJ fanboy as well.)
Jeong Jeong is around 60 years old, has two vertical scars next to his right eye, and is a master firebender. However despite his awesome skills, he does not think highly of Firebending and sees it as a "burning curse". In a conversation with Katara, he admitted that he had always wished that he were blessed with Waterbending skills instead.
He described Firebending as something that "brings only destruction and pain. It forces those of us burned with its care to walk a razor's edge between humanity and savagery. Eventually, we're torn apart."
Long ago Jeong Jeong had a pupil, Zhao, who did not improve his thoughts on firebending in the least, and may have even contributed to them. Zhao was only concerned with the power of firebending and how to destroy his opponents and the obstacles in his path. He held no regard for learning the discipline that came with it, much to Jeong Jeong's disappointment.
When Aang was brought by Chey to Jeong Jeong's camp in order to learn firebending (in ep.16), Jeong Jeong was furious because it was clear to him that Aang was not ready. He could tell just by watching Aang walk into the camp that he had not mastered Waterbending and Earthbending, whose disciplines would aid Aang in controlling the power of Firebending. Jeong Jeong only changed his mind on teaching Aang after receiving a chilling vision from Avatar Roku.
Jeong Jeong's teaching techniques rest heavily on discipline. Before the pupil can learn how to make fire, he must first understand the elements to controlling that power. Because Firebending draws its strength from the breath, the pupil needs to master proper breath control (By inhaling through the nose, and exhaling from the mouth). Another part of learning control is to concentrate, while the preferred stance is legs wide apart and knees bent. Holding this stance for long periods of time while meditating or in Aang's case, concentrating on the sun's warmth, is an excellent way to strengthen the mind, body, and one's discipline. When Jeong Jeong feels that his pupil is ready, then they can learn how to firebend, and even then the steps are slow and careful.
Jeong Jeong only managed to train Aang for about a day before Zhao and his men showed up, but he taught Aang many valuable lessons. And although Jeong Jeong and his followers (except for Chey) vanished without a trace, I believe they will return in the future.