In Imperator: Rome, each city has its own population, which is measured in terms of population units - "Pops" - divided into 4 classes/categories. This is a significant difference from other Paradox games where the population was counted in large statistical numbers; this system is very similar in population distribution in Stellaris.
In each city there are always 4 categories of residents:
Citizens - affect trade and the acquisition of new technologies, represent patricians or the nobility, depending on the region.
Freemen - their number depends on the amount of human resources. They can be compared to the plebes in Rome.
Tribesmen - have little impact on tax income and human resources. They are either barbarians or uncivilized inhabitants of a given region.
Slaves - affect primarily the income from taxes, they are the backbone of your economy.
Happiness of the citizens affect their productivity. The citizens can become unhappy if they are not a part of the same religion or cult in your country. Aside from that, the dissent can increase through the current governor, the current level of stability in your country or the tyranny factor. Higher the happiness and productivity, the more taxes or manpower you'll receive.
The inhabitants of this province are not the happiest they can be, but if you'll manage to sway at least a few of them to Hellenic faith and assimilate them with the Roman culture, they can become very happy and productive.
When you choose the portrait of the given social class, you'll enter a screen that will allow you to assimilate subjects, convert them to a different religion, advance them to a higher social group, or let them migrate to a different city. This way, you can quickly increase the happiness of your population. On the other hand, some bonuses are awarded to the inhabitants of other cultures. Some discoveries, laws, events, or products can change the happiness bonus for every social class.
You can gain new inhabitants by providing certain resources or conditions to grow. After a certain period of time, you'll receive a new unit of population. You can notice it through green plus symbol on the icon of the given class and the change in the growth bar underneath such icon.
Other ways of gaining population are conquest and fighting barbarians. This is the best way of gaining a lot of slaves. Conquest of a town can lead to rewards in form of citizens. Most of the time, conquering a city with a fort will yield new subjects. Some large cities or historic locations have their own event that will allow you to decide upon the fate of the inhabitants. Remember that after a won battle, new citizens land in random capitals (cities with the pillar symbol). These cities will often grow in number.