The population of a city is the number of citizens living there. It is displayed at the top of each city dialog's overview tab. It is given by a formula depending only on the size of the city:
$ population = \big\lbrack citySize*(citySize+1)*5\big\rbrack*1000 $
The population of a civilization is the sum of each of that civilization's city's populations. Examining these numbers provide an indirect way of comparing different civilization's city sizes. When computing this value, fewer cities with larger sizes will give larger overall populations than more cities with smaller sizes (e.g. one city of size 8 will contribute 360,000 to a civ's population while 8 cities of size 1 will contribute 80,000).
Your civilization's total population can be checked in the Demographics Report.