Populating is the act of placing Citizens inside a Settlement, Town Center, Capitol or Granary in order to increase the resource gain from each building or to turn it into a different building. To populate a building, select the desired number of citizens, click the button next the Explore button and then right-click on the building you wish to populate. You could also just press "G" on your keyboard instead of clicking the populate button.
A Settlement requires 5 citizens to become a Town Center, which in turn becomes a Capitol once 15 citizens are inside. A Capitol can then house a total of 50 citizens. A Capitol gives a resource bonus of 100%, which means 15 units of resource will convert into 30 units once inside the Capitol. However, this only works for Stone, Iron and Gold.
Granaries can be also populated with 8 citizens to form a Granary - Improved. Thus a citizen droppoff of 15 units of Food will convert into 19 units.