Population refers to how many people live in either a city or a Provence. In some Total War games it is very important, in others it does not matter very much at all, and in some it is not represented.
Rome Total War
In Rome Total War, each settlement has a certain population. Population is essential to develop settlements. Settlements range from Villages to Towns, Large Towns, Minor Cities, Large Cities, and Huge Cities. Upgrading a settlement to the next level allows the settlement to build more important buildings. Population is required for each upgrade beyond a Town, 2000 to upgrade to a Large Town, 6000 for a city, 12000 for a Large City, and 24000 for a Huge City.
Population is lowered by recruiting Troops and Agents. It is also reduced drastically if there is a plague; plagues are more likely to occur in regions with High Squalor and less likely to occur in regions with high Public Health. Population growth is increased by building buildings such as Farms and Public Health buildings. Regions that have fertile soil will automatically have higher population growth.
Enslaving enemy cities will also take half of the people from a conquered city and divide among all of your settlements with a governor (or among all of your settlements if no city has a governor). Enslaving cities also creates a slave resource on the map that improves population growth of nearby cities.
When you conquer an Large or Huge enemy city, it usually has terrible public order. It may be necessary to Exterminate it, killing 75% of the people and plundering their wealth, in order to keep it under control. A horde in Barbarian Invasion can also Sack a settlement, doing much the same thing.
Apart from settlement development, population has some other effects. Increasing the population of a settlement increases the Trade and Tax income of the settlement. It has progressively diminishing returns; adding 1000 people to a settlement with 2000 people will add much more income than adding 1000 people to a settlement with 11000 people. Additionally, cities with high population develop a lot of squalor and troops have less effect on them, making public order difficult to control. Once your settlement is a Huge City, it is usually best to not try to grow the population any further.
Medieval 2: Total War
Like Rome Total War, In Medieval 2 Total War each settlement has a certain population needed to develop settlements. Settlements are the same a Rome except castles are added. Upgrading a settlement to the next level allows the settlement to build more important buildings. 800 Population is required to upgrade a Village to a Town, 2000 to upgrade to a Large Town, 6000 for a city, 12000 for a Large City, and 24000 for a Huge City. No population is needed for Wooden or Stone Castles, but a Fortress needs 4500 and a Citadel needs 9000. Unlike in Rome Total War, these values are not hard coded.
Population is increased mostly by building farms and Town Hall style buildings. Additionally, a Chivalrous governor can increase the population by 0.5% per turn for every point of Chivalry. There is no slavery mechanic in Medieval 2 and recruiting does not lower the population either. Sacking a settlement replaces the enslave option from Rome Total War. It steals a lot of wealth and kills 20% of the people. Other than that population works exactly the same way.
Squalor is lower in Medieval 2 than in Rome, so overpopulation of cities is less of a concern and exterminating enemy settlements is rarely necessary. Squalor also has a cap, so if a settlements growth is extremely high it might not stop growing. When this happens the settlement will become more and more profitable. In the vanilla game the absolute settlement max is 216,000 people.
Empire: Total War
In Empire Total War, population shows the amount of people in a region, not the capital city. Regional population is increased by building food production buildings, by researching technologies, and by cutting taxes on the Lower Classes. It is decreased by 0.05% every turn for every enemy unit that ends a turn in the region.
Population growth allows villages in the Region to become Towns. Once they are Towns, they can build some sort of building. Coastal Towns can build a port, Land Towns can build a Religious, Cultural, Educational, or Economic building.
A regions with higher population also takes longer to Convert, spawns more Armed Citizenry when attacked and is more expensive when it has to pay for Town Watch. These effects are very minor, making population mostly irrelevant once all the villages have developed into Towns.
Napoleon: Total War
Population is mostly a leftover from Empire Total War and functions exactly the same way. However, there are no villages in Napoleon, and no religious conversion (except in the Peninsular campaign). This makes population largely irrelevant. It is only effected by the Tax Rate on the Lower Classes and by enemy armies in a region.
Shogun 2: Total War
There is no population mechanic in any Shogun 2 campaign.