On top of simply mastering all four of the elements, Aang's inevitable goal is to also master the Avatar State. As the Avatar, Aang has access to the skills and experiences of the hundreds of Avatars who preceded him. Tapping into these things, however, requires him to enter the Avatar State. Without proper training, this powerful transformation acts as more of an instinctual, reactionary emergency button. If Aang is in any serious danger or stress, he loses his self-control and will enter the state without warning.
While in the Avatar State, Aang's powers are all magnified by the skills of those who came before him. Likewise, he gains access to bending techniques that he is unaware of. An Avatar in the Avatar State can split islands off the mainland, fly, and bend all four elements simultaneously. The Avatar State remains Aang's most powerful weapon up until the very end of the series, when he learns something entirely new.
