The thing I loved most about Avatar (and The Legend of Korra) is the emotional depth to characters. I never got that in media I was allowed to consume as a kid, and I'm glad that that's different for some people!
I did appreciate that this series spent a considerable amount of time exploring ethics and character development in ways that a lot of cartoons I watched growing up didn't. But due to the target audience a lot of that exploration was very surface level though, especially compared to the overall setting that the story takes place in and some topics, such as the genocide of the Air Tribe or how the main hero Aang literally destroys fleets of ships with little effort and how whether or not he's wielding such power appropriately, aren't really concepts you can delve deeply into in a children's show with ease. That's not to say that the creators did a bad job telling a story, but man, the themes of this series are actually very big. Now, to their credit, there are tons of shows and movies aimed at adults that touch on similar themes and don't even give them the exploratory consideration they deserve. So to get even the level we did in Avatar is kind of impressive, even more so since it was made about fifteen years ago.