Opening sequence

The opening sequence of Avatar: The Last Airbender is played at the beginning of every episode.

Sequence
The show opens by showcasing the various bending methods: Waterbending, Earthbending, Firebending and Airbending, with each being done by a character seen in the series. The Waterbending is done by Master Pakku, the Earthbending by Sud, the Firebending by Azula, and the Airbending by an anonymous monk. The monk was thought to be Aang, until it was noticed that he had a moustache. It then shows the map of the Avatar World. After that, Katara explains the Fire Nation attack. Following this, Avatar Roku can be seen using all four bending methods and disappearing in a gust of air when Katara says "he vanished." Next, Katara and Sokka are seen, then Aang, showing scenes from the first episode. The title card is shown immediately after. The Chinese characters that appear at the top of the show's title card mean "the divine medium who has descended upon the mortal world."

Narration
Katara narrates the opening sequence. In the first episode, she states:

"'Water. Earth. Fire. Air. My grandmother used to tell me stories about the old days, a time of peace when the Avatar kept balance between the Water Tribes, Earth Kingdom, Fire Nation, and Air Nomads. But that all changed when the Fire Nation attacked. Only the Avatar mastered all four elements. Only he could stop the ruthless Firebenders. But when the world needed him most, he vanished. A hundred years have passed and the Fire Nation is nearing victory in the War. Two years ago, my father and the men of my tribe journeyed to the Earth Kingdom to help fight against the Fire Nation, leaving me and my brother to look after our tribe. Some people believe that the Avatar was never reborn into the Air Nomads and that the cycle is broken, but I haven't lost hope. I still believe that somehow the Avatar will return to save the world.'"

Every episode after that, she says:

"'Water. Earth. Fire. Air. Long ago, the four nations lived together in harmony. Then everything changed when the Fire Nation attacked. Only the Avatar, master of all four elements, could stop them, but when the world needed him most, he vanished. A hundred years passed and my brother and I discovered the new Avatar, an Airbender named Aang. And although his Airbending skills are great, he has a lot to learn before he's ready to save anyone. But I believe Aang can save the world.'"

In the first pages of "The Promise Part 1" Katara says :

"'Water. Earth. Fire. Air. Long ago, the four nations lived together in harmony. Then everything changed when the Fire Nation attacked. Only the Avatar, master of all four elements, could stop them, but when the world needed him most, he vanished. A hundred years passed and my brother Sokka and I discovered the new Avatar, an Airbender named Aang. Although his Airbending skills are great, he had a lot to learn before he was ready to save anyone. But from the first day I met him, I believed Aang would save the world. And you know what? I was right. With the help of his friends, Aang defeated Fire Lord Ozai and ended the Hundred Year War. Zuko, Ozai's son and our ally, became the new Fire Lord. Together with Earth King Kuei, Aang and Zuko promised to return the Nations to harmony.'"

Calligraphy
In this sequence, the calligraphy for each element's bender shows something about it. On water, it says 善水 -"Water is generous." Earth says 強土 - "Earth is strong." Fire says 火烈 - "Fire is vigorous" and Air says 和氣 - "Air is peaceful." In the opening title card, Where it says 降世神通 - "Avatar: The Last Airbender," above it, it has calligraphy saying, "The Holy Medium Descended Upon The Mortal World," thus referring to the Avatar.

Trivia

 * The Airbender seen at the start of the sequence has been speculated to be either Aang, Gyatso, or a random Air Nomad. The main argument against it being Aang is the fact that the Airbender displayed has a moustache, while a few of the arguments against it being Gyatso are the fact the figure isn't wearing his robes and the obvious age difference. In either case, the true identity of the silhouette has never been credited by the makers of the show.
 * Along the words, "Everything changed when the Fire Nation attacked," a line of Firebenders is shown as they are seen in the series. However, the War began one hundred years prior to the first episode, when the Fire Nation's armor supposedly had large shoulder spikes and a faceless helmet, according to Chief Arnook.
 * For unknown reasons, Azula bends a normal colored fire rather than her trademark blue fire. This may be to show "normal" Firebending.
 * The unknown monk Airbending is the only character in this showcase of bending skills who was not shown in this series.
 * In the The Last Airbender: Legend of Korra trailer, Korra is seen Waterbending in front of a backdrop similar to the backdrops seen in the Avatar: The Last Airbender opening sequence. It is possible that this is a clip of The Last Airbender: Legend of Korra opening sequence.