"Avatar: The Last Airbender" explores themes of identity and self-discovery through the journey of the main character, Aang, who is the Avatar. Throughout the series, Aang grapples with understanding his role as the Avatar while also trying to figure out who he is as an individual. The show delves into Aang's past, his struggles, and his growth as he embraces his identity and learns more about himself. Additionally, other characters like Zuko and Katara also go through their own journeys of self-discovery, adding depth to the exploration of identity in the series.