Growth = Amount population increases per season.
Growth is not affected by production. In Legendary Heroes, you will have the option to cut off production in a city to increase growth by 50% for however long you like. Your population will always increase by your Growth amount each season.
Population is capped by the amount of food. You can have up to 1 population per 1 food. Increase food production and you increase the cap.
In Legendary Heroes, there is a growth bonus (up to +3) for having excess food. Prior to that, the only way to increase growth was by building improvements that increase growth, using city enchantments that increase growth (I can only think of the one in Life Magic), and by having a Governor champion stationed in the city.
At level 2, you choose whether the city becomes a Town, Fortress, or Conclave. Each of these has a bonus described at the time of selection, and there are buildings specific to each of these types. Towns have improvements that increase Growth and Food Production (the Grocer chain of improvements increases food production in all cities, not just the one you build it in). Fortresses have military-focused improvements. Conclaves have improvements that increase Research and Mana production. Every level afterwards gives you another choice of 3 benefits along that chain, up to level 5.
Higher level cities also have more defending units. Level 1 city gets 2 militia. Level 2 city gets 3 militia and 1 archer. Each level up you get more militia and archers. These defenders cannot be moved from the city, but do not cost wages, nor contribute to the city occupancy limit (you can only have so many units stationed in a city).
