Why does economic growth or increases in real GDP such a good thing? Is it because unemployment generally goes down when GDP rises and spendingand incomes rise?
Yes, that is pretty much it.
The assumption is that it is better to have more money rather than less. When the Real GDP of a given country goes up, the people of the country are more likely to be well off. Unemployment generally goes down. Economic growth does not have to go along with a decrease in unemployment, but it usually does. When people have more money and when more people have jobs, people's lives are, for the most part, better.
Economic growth just makes for happier, less stressed people in general and that is a good thing.
Growth in an economic or increase in real GDP means that the combined value of the products and services generated in the economy and available to the people for consumption or for increase in wealth through export has increased. In other means that people in generally are economically better off. This is why economic growth and increase in real GDP are considered good for economy.
Such growth is usually accompanied by increased employment. Which is also good for the economy, because it means that the increased prosperity of the economy is being shared more widely by the members of the economy. However, theoretically it is possible for economic growth to be accompanied by reduced employment.