Why is it that countries all over the world try their very best to increase the value of GDP, GNP, and GNI?
GDP (in a closed economy) is the sum of consumption spending, investment spending and government spending.
Higher GDP means people can in aggregate buy more goods and services (eg Go on more vacations, buy more education, more healthcare etc), invest more into their businesses that allows country to produce more in the future (eg build more factories) and to spend more on public services.
Generally people prefer to be richer than to be poor. GDP is not just sum of all spending but also sum of all incomes (someone’s spending is always someone’s else’s income). Similarly as you as individual would (likely) prefer to have higher yearly income, all else equal, than to have low yearly income, countries prefer to have higher GDP to low GDP.
GNP and GNI are just different way of measuring the above, so the same explanation applies.