Person of Asian decent who is also an American citizen. There are many different Asian Americans. Some have ties to their respective countries in Asia, some don't, and some find a middle ground.
Japanese American, Chinese American, Indian American, Korean American, Vietnamese American, etc...
I am an Asian American.
An Asian person who was not born in the U.S. but emigrated instead, and has become a "naturalized" citizen.
I am an Asian American. I was born in Asia and migrated to the U.S.