Economic growth is best defined as an improvement in real GDP per capita, which essentially refers to the value of all of the goods and services produced in a country per year divided by its population.
The reason why economists use this metric is that it is easy enough to calculate and it reflects the standard of living with relative accuracy. In particular, it is adjusted for metrics such as population (if the same amount of goods are split between more people, each person doesn't have as much) and inflation (even if people are making more money than before, it doesn't help them if that money is worth less).
However, it is not perfect--GDP omits household production, which is when you produce goods and services in your own home without any formal payment (e.g. you cleaning your house, your parents cooking a meal, etc), trades conducted off-the-books (e.g. bartering), and illegal/black-market production. Moreover, real GDP per capita disregards income inequality--if a few people hold all the wealth, the country is worse off than if the wealth is distributed roughly evenly.
