Province population that is of use to a player is divided into three types, representing three different socioeconomic strata in the ancient world.
Ranking just below your pictured nobility class are those wealthy enough through their provincial holdings to have a great amount of free time available to contemplate the problems of the universe. This strata generates the research potential of the province. The number of citizens in a province is also increased by converting a percentage of your freemen into citizens, at a yearly rate determined by your laws and the citizenship national idea.
These are the trades and craftsmen of the province. They are not a good source of tax monies, however their numbers provide the raw material for the legions.
The lowest rung are those bound to the latifundas, mines, and manufactories owned by the Citizen class. This strata provides the tax base for the province.
Destroying a barbarian army will allow you to capture them as slaves, generating 0.1 population points of slaves per regiment. One third of these will go to your capital with the rest being evenly divided among your provinces. "Farming" barbarians will allow even a small state to build up a good income from slave population and these can be converted to Freemen for manpower with the emancipation national idea.