From an early age, Aang is taught by the Air Nomad monks to revere life. He grows up loving life. He's typically very easy to get along with. He's a pacifist, refusing to take life or even to eat meat.
However, he also has an irresponsible streak. He has a tendency to avoid his problems, and he's overactive to the point of being obnoxious. If he wants to save the world, he'll have to do a little growing up, first.
His Life(Major spoilers ahead)
Before the Show
Aang, as the Avatar, is an incarnation of the earth spirit. Born an Air Nomad just after the death of his predecessor, Aang became the youngest ever to master airbending. Because of the political instability of the era, the Air Nomads told Aang about being the Avatar years before he was ready, and he ran away just before they could separate him from his mentor, Monk Gyatso.
Riding his sky bison (Appa) into the unknown, he runs into a deadly storm and crashes into the ocean. Just before drowning, the Avatar State activates and freezes both him and Appa in a ball of ice. Season One
Aang is somewhat conspicuous.
Aang is saved a hundred years later by Katara and her brother, Sokka. At first, Aang neglects to mention that he is the Avatar, and the two siblings take him back to their home in the Southern Water Tribe. However, he attracts the attention of the near-by Fire Nation Prince, Zuko. Sokka, the de facto 'Man of the Tribe' banishes Aang out of anger, but when Zuko finally shows up and starts terrorizing the village, Aang returns and surrenders himself.
Katara and Sokka, now realizing that Aang is the avatar, rush to save him, and Aang promptly takes them on a journey to his old home, the Southern Air Temple. Here, he is finally forced to recognize the reality of his situation. He mentor Gyatso is dead, murdered by Fire Nation soldiers in the Air Nomad genocide. They slowly begin making their way to the Northern Water Tribe in hopes of finding a master waterbender for both him and Katara. He does waste a lot of time, though. He continues to avoid his responsibilities as the Avatar until, he discovers a forest burned down by Fire Nation troops for seemingly no purpose. Because of his disappearance, he blames himself for the current state of the world. This sparks a journey into the spirit world, where he meets his predecessor, Avatar Roku. Roku gives him the facts. By the end of the summer, a comet will come and give fire benders unimaginable power. If Aang is going to save the world, he must do so before that time. Realizing that he has less than a year to complete this goal, Aang and his friends continue to make their way north.
Along the way, puberty hits, and Aang realizes that, hey! Katara's kinda cute! Not only that, but he starts to grow very attached to both of his new friends. When a messenger brings news to him that might cause them to leave, he hides the message from them. When Aang finally breaks and gives the information out, his companions are understandably ticked. They are about to leave, but events bring them back together. The two forgive Aang, who felt terrible about the whole thing and perhaps became a little less selfish because of it.
Beware the Face Stealer.
Eventually, they do make it to the Northern Water Tribe. Aang and Katara find Pakku, a master water bender, but the city is soon assaulted by a large Fire Nation fleet. Aang decides to enter the spirit world, hoping to get advice from the Moon and Ocean spirits. Avatar Roku directs him to an ancient spirit, Koh, the Face Stealer. At the slightest display of emotion, Koh will steal your face.
But he is one of the oldest spirits around, and only he knew what happened to the Moon and Ocean spirits.
Eventually, he reveals that the moon and ocean spirits where there in the phsyical world the whole time. But Zuko has stolen Aang's physical body, and before he can return, a Fire Nation Admiral, Zhao, has taken the moon spirit captive and eventually kills it. Aang allows the Avatar Spirit to be taken over by the Ocean Spirit, and as a giant glowing koi fish, he destroys the attacking fleet.