Every city's resident can be put into work on one of the 17 tiles in city reach.
Tiles give Food eaten by citizens, Production used to build different structures and military units and commerce spend on research or put into empire treasury.
Every tile which generates less than 2 Food is slowing city growth because residents working there eat more Food than harvest itself. When the tile isn't generating Food at all, the situation is as if this citizen would have been a specialist - it means that he has to be fed completely by another city resident's work.
This is the reason to aim in at least small surpluses of Food - this makes possible to have specialist and use tiles generating no Food. In this helps Food generated by city itself - it's especially useful when city is small.
In emergency, particularly when you have a granary and huge amounts of Food in city reserves, it's acceptable to allow a few turns of Food deficit when you use your citizens in more important duties.
As a side note - city governors are quite helpful for the people who don't like micromanagement. You can set priorities (emphasise grown, Production, research and so on) and amount of power which governors have and city will be developed without our constant attention. However, I suggest a limited trust and using this tool only in cities without strategic importance.