(About city specialization, specialists and the City Screen)
The white circles on the tiles are what is being worked on at the moment. The city will only get the yields (in terms of

,

and

) from those tiles and not from any other tiles. The number of tiles worked is the same as your city size. So each populations point corresponds to one "Citizen".
By clicking on the marked tiles (still inside the City Screen) you remove that Citizen from working the land. It has now become a specialist and can be found in the right side panel as a plain "Citizen" specialist. This isn't a very good specialist (with only a +1

), so you should probably click on another tile to put him back to work on some tile instead.
But if you do have the option of assigning other more useful specialists - like Scientists or Merchants - you can make that Citizen into a proper specialist by clicking on the "+" symbol associated with the type of specialist you wanna employ.
You could remove all citizens from working the fields and make them into specialist (even plain Citizen ones if you lack other options) if you wanted. This would, however, starve your city down to size 1 and this way you'd end up with only one specialist in the end. So don't even consider this as any kind of option!
One thing you also have to understand is food production

food

. The

collected from the tiles your citizens are working is stored in the Food Bar at the top of the City Screen. But firstly you have to feed your populous and every population point requires 2

per turn - otherwise the city will starve. This is why the

surplus per turn is shown in the City Screen - can you find it?
So, its actually the surplus

that gets stored every turn and when the Food Bar is full the city grows by one population point. The Granary building effectively cuts this time in half by storing half of this amount every time the city grows. Otherwise its all gone and you'd have to fill it up again from nothing.