Used humorously, to go native means to take on some (or all) of the culture traits of the people around you, often said of people who go to foreign countries or far away cities. These traits may include dress, language, accent, etiquette, religion, etc.
Important: The common use of the phrase does not have anything to do Native Americans.
1: When he visited China he loved the culture so much that he disappeared and went native.
2: Better keep her away from the village. She might just go native on you.