What does population do?

The population affects the mint gold income. Although it will depend on how much your mints are upgraded whether you will notice an effect on the production rate. You can tap on the gold display in the top right to see your current production rate and the efficiency. If this is below 100% then you need more people in your city to improve it.

If you do not have your mints fully upgraded or if you are not currently in need of a high production rate then you don't need to maintain the population.

You will also find that some of the upgrades for your castle and some other buildings will require a minimum level of population to start. But once they are started you do not need to maintain this.