For a quick reference:

Level 1 cottages offer 100 population.

Level 2 cottages offer 300 population.

Level 3 cottages offer 600 population.

Level 4 cottages offer 1,000 population.

Level 5 cottages offer 1,500 population.

Level 6 cottages offer 2,100 population.

Level 7 cottages offer 2,800 population.

Level 8 cottages offer 3,600 population.

Level 9 cottages offer 4,500 population.

Level 10 cottages offer 5,500 population.

If I had 2 level 7 cottages, 5 level 4 cottages, and 1 level 9 cottage, I would have a total population limit of 15,100 people.

How come I don’t have a population of 15,100 then?

The reason is because of your tax rate. If my tax rate was 0%, then I would indeed get 15,100 people. If my tax rate was 10%, then I would have 13,590 people (90% of my population limit).

Now population is used for two main things: Workers and Troops for your army.

In any city, you need people to work in your farms, sawmills, quarries, and ironmines. Therefore, with each resource building that you build, you a certain portion of your population goes to work.

The remaining population is used to train, or recruit, troops. If I had 5,000 idle population, I have the ability to create 5,000 men. Of course, since troops such as archers take “2 population” I can only train 2,500 archers.

Yes, your population does replenish after you train troops – it just takes a short period of time.