Construct buildings from the “Infrastructure” tab and complete the Super-quests (Superzilla, Nessie, Genie, etc.) to increase your population limit.
After that, building new houses will attract new citizens to your city.
Once you get the correct population that a building says, then it will unlock for you and then you can buy and place them.
Example: Here you can see that the coffee shop needs population of 400. Once you have enough population, then it will unlock for you.