Aang is biologically 12 years old when Avatar: The Last Airbender begins.
The key distinction is between Aang’s biological age and his chronological age. He is 12 in body and development, but he has technically existed for 112 years because he spent a century suspended in an iceberg before Katara and Sokka discovered him.
Aang disappeared shortly before the Fire Nation’s genocide of the Air Nomads. The iceberg preserved him for 100 years, while the world changed around him. When he awakens, he initially does not know that the war has lasted a century or that he is the last surviving airbender of his people.
That unusual age gap explains much of the story’s emotional tension. Aang is expected to master all four elements and confront Fire Lord Ozai, yet he remains a child carrying responsibilities created by events that began before his birth. Later, in The Legend of Korra, his official age is again discussed using both chronological and biological measures.