The Avatar State
At first, the Avatar enters the Avatar State when they are under incredible emotional stress or when they're in peril. But, it is possible for an Avatar to master the Avatar State.
When an Avatar enters the Avatar State, his eyes glows, and in the case of Airbender's, they're tatoos glow. This is because the Avatar is channelling the knowledge of all his/her past lives. The knowledge gives the current Avatar the ability to bend all the elements, because of the mastery of their former lives.
Even though the Avatar is at his/hers most powerful when they are in the Avatar State, they are also at their most vulnerable. If the Avatar is killed when he/she is in the Avatar State, the Avatar cycle will be broken, and the Avatar will no longer exist.
Aang was in the Avatar State when he and Appa were frozen in temporal statis, as he used it to save Appa and himself when they were about to drown.
Book One: Water
Aang entered the Avatar State in the next episode, used to save himself from drowning (yet again) and defeat
He then entered the Avatar State when he discovered Monk Gyatso's corpse, but was calmed down by Katara.
Aang didn't access the Avatar State again until the finale of the first season. After the Moon Spirit was killed, Aang entered the Avatar State and merged with the Ocean Spirit, and they brutaly attacked the Fire Nation.
Book Two: Earth
The Avatar State was one of the main focuses of Book Two: Earth. In the first episode,
and his soldiers tried to get Aang to enter the Avatar State, to use it as a weapon to take down the Fire Nation. General Fong eventually manages to shock Aang into the Avatar State, by making it look as if he killed
. Aang refuses to use the Avatar State to attack the Fire Nation then, because of all the people he hurt.
Aang later entered the Avatar State when he found the Sandbenders who took Appa, but he Katara managed to calm him.
Near the end of the season, Aang is contacted by Guru Pathik, telling Aang that he can help him master the Avatar State. Aang visits Guru Pathik, and Aang opens six of his chakras, but he refuses to open the final one because he would have to let go of Katara.
In the season finale, Aang opens the seventh chakra, and enters the Avatar State, but is struck down Princess Azula. When this happens, Anag's seventh chakra was locked, and he can not enter the Avatar State at this point in time.
Book Three: Fire
Aang is no longer able to enter the Avatar State, because of his injury he recieved from Azula.
Uses in past lives
Avatar Roku entered the Avatar State when he attempted to stop the volcano on his island, Roku Island, from erupting
Avatar Roku used it to fight Fire Lord Sozin
Avatar Roku spent five months on Crecent Island trying to master the Avatar State, with Fire Sage Shyu. He became impatient and used the sun light during the winter solstice to speed the process up, but he lost control of his body, and destroyed the temple. Luckily, Fire Sage Shyu reflected the sun light away from Roku, releasing him from the Avatar State.
Avatar Kyoshi entered it to seperate Kyoshi Island from the main land