The literal definition is 'North American', applying to residents of all of the countries of North America. However, typically it's used as a more politically correct way of saying 'from the United States' because in Spanish America does in fact refer to two continents comprising of 35 countries, not just one. Central and South Americans might take exception to the usage of 'americano' because it insinuates that they are not Americans as well.
Many people would rather use Indian as it is shorter, but indeed it is more correct to use the above term. Thus, we result in a compromise.
Bob: "Hey, Did you see that new kid at school? I think he's an indian"
Steve: "Nah man, He's a native american."
Bob: "Right, or we could just call him a namerican."