Population Growth is one of the two rewards you can choose after you have upgraded a level 3 city to level 4 (the other being Border growth). It immediately gives the city +3 population. Also, it is also one of the rewards obtained from examining ruins. It immediately gives your capital city 3 population. If your capital has been taken, and you get population growth from a ruin, it will go to the highest level capital you have. You can’t get it from a ruin if you don’t own a capital.

If received from a ruin, however, the upgrade is presented not as a natural increase in population within your city, but as a nomadic people who settle in your capital.