Cottages in Evony are probably the most basic building that you can construct. They have one purpose: to house any people who want to live in your town. The more cottages, and the higher level each cottage is, the more population you can obtain.
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.