Without trying to get into studies, theories, generalizations, and whatever else someone may factor in when drawing that particular conclusion; one point is that there are different types of intelligence. In families where high academic achievement is valued children are more likely to achieve in school.
There are, however, different types of intelligence; and if it's true that many Asian students excel in some subjects, like Math; the other side to that is they may not do as well in some types of thinking as some American children do.
Many Japanese mothers, however, focus very much on remaining in one-to-one contact with their child and on teaching them a number of different things from the time they're babies on. So, in that kind of situation it would be simply be all that one-on-one teaching and attention a child gets.
I don't want to sound obnoxious, and I'm only going to say this to back up my point; but I think it's too much of a generalization to say that Asian children are more intelligent than American children. Based on my own (grown) kids' intelligence, academic skills, many talents, and social maturity when they were young; (and based on a lot of the very intelligent and similarly talented kids I met through their friends or my own) there are a lot of pretty darned intelligent American kids. One problem may be that a lot of people don't talk about all those intelligent and achieving American kids because they think nobody has to worry about them. Instead, we hear about all the American kids who do well enough but don't excel, or else who don't do well at all. If you send your American kids into public school, where they're several grade levels ahead, nobody wants to talk to you about meeting their academic needs because people think there are no particular needs for kids who do that well. So one problem in America may be the public schools and the apparent favoring of slightly above average, while placing lots of attention of those students who are average or below.