"Why is 'growth' in GDP important? If GDP can be kept constant every year (that means zero growth rate), what's the problem to the country or even to the world?"
That's a great question that gets at the very core of economics. Generally we accept in Economics that increases in wealth, income, and consumption levels are desirable. That's because we view consumers as being utility maximisers, who derive increased utility from increased consumption. In such a model of the world, increased GDP implies increased utility. If the role of Government is to maximise the welfare (utility) of consumers, it should institute policies that are therefore consistent with maximum growth rates.
So given our model of the world, consumers have higher utility the higher is their consumption level. But utility is unobservable, so we cannot directly test this hypothesis. Most reasonable people would agree that at low levels of income, an increase in income clearly makes people better off. They are able to eat better food, live in a more comfortable physical environment, enjoy better health, and generally suffer less throughout their life. This is the stage of development for many parts of rural mainland China to this day.
But once we have all our basic human needs met, are we still better off with economic growth (i.e. increased incomes and consumption levels)? That may be disputed by some, although I can assure you, that at the margain, I think I would be happier with a better car, a nicer flat, or more holidays.
But maybe this is delusional. I also observe people who seem to be fully content with their current modest standard of living, and appear to be making no effort to improve upon it. My interpretation of this is that learning to be content with your standard of living is itself an important contributer to enjoying a high level of utility.
Following this argument, if contentment matters more than growth for welfare once basic human needs have been met, then Governments of developed economies maybe should focus less on growth and more on other matters that play an important role in welfare, like the environment.
I'm weary of that conclusion, however: many of the steps that I would advocate a Government to take in order to encourage economic growth (efficient Government, good health care and education, property rights, democracy) are good in their own right, and make people better off independent of their effect on economic growth. The fact that they happen to encourage economic growth is an added bonus.