Population is a term used in Civilization V to represent the Citizens living in each of the population centers (cities) of the civilization. Citizens are the main laborers of the empire, working the tiles of terrain around the city, as well as the Specialist slots, to obtain yields. As such, they're paramount for the productivity of each city, and the empire as a whole.
Population is represented by a number that indicates both the number of Citizens inhabiting a city and its general size. This number is not literal, and is instead used for gameplay purposes: an individual Citizen can work one tile, or use one Specialist slot, or be Unemployed. If a city has 1 Population, or a single Citizen, it does not mean there is literally only one person living there; it means the city is a very small village. A city with a Population of 10 is a concentrated urban area, and a city with a Population of 20 or more is a major metropolitan area. The size differences between cities are represented graphically as well: whereas a newly founded village will barely occupy the middle of its tile, a sprawling metropolis will appear to spill over into neighboring tiles.
Each new city starts with a Population of 1, or 1 Citizen. This means that it can work one nearby tile (in addition to the tile the city is placed upon, which is worked for free). It can subsequently grow or shrink its Population according to the rules of Food consumption and distribution, though it will always have at least 1 Citizen.
Apart from producing tile yields, Citizens also contribute to Science production at the rate of 1 Science per Citizen without additional buildings. Each unit of Population produces 1 Unhappiness, and so Happiness serves to cap the number of Citizens in the empire.