I think you start with a population of around 100-150. Go to Tools-> achievements to see how much you currently have. You can build clay huts to increase your population. To do so go to Tools-> Shop -> population. A clay hut will cost 5600 coins and increase your population with 50. I progressed through the quests and build a total of 3 clay huts, and this gave me the achievement. ( I think your population also increases a little by doing quests or just over time).
You can see your progress if you press Tools-> Achievements. Once you reach 300 or more, the achievement will pop.