Approval rating is the percentage of all your people who are happy. Or rather, the average happiness, with unhappy being 0%, happy being 100% and content/specialists being 50%.
Population is the sum of all the populations of your cities.
GNP is the total raw tax income of all of your cities.
I think Manufactured goods is the total non-wasted shield output of all of your cities.
Land Area is proportional to your territory, surprisingly enough.
Literacy is an average of all your cities' literacy, which is computed thusly: The literacy tech gives you 3%. Each of Library, University and Research lab adds 33% to that city, as do each of the +Sci wonders (Newtons, Copernicus', SETI). This is why it always goes down when you invade people. Maximum is 99%.
Disease is the % of your population who live in a city with Jungle or Flood Plains in its radius.
Pollution is the number of squares of pollution in your territory.
Life Expectancy is calculated similarly to Literacy, except it checks for Granaries, fresh water/aqueducts and Hospitals instead of science buildings. Max is 99 years.
Family size is the average food surplus of your cities, divided by two.
Military service is something like the number of military units you have x10, divided by your total population (in points).
Annual Income is proportional to the number of strategic/luxury resources you have connected to your capital, plus a bonus one for your first trade of either of those with another civ.
Productivity is a measure of the total useful output of all of your cities, in food, shields and trade, though I forget how it's worked out exactly.
Oh, and top 5 cities is easy: It's the top 5 cities in terms of accumulated culture. In the event of a tie, it then goes by size, and if it's still tied, more recently founded cities go higher.