One of the most important factors of your success is level of infrastructure development. In CIV it is essential to control some well developed and highly advanced cities as foundations of every advanced strategy.
In CIV it is possible to specialise cities - focus them mainly on one function. It's not obligatory and especially on lower difficulties (up to noble) it is possible to win without even trying to specialise. It's very helpful nevertheless - as in real life focusing on some kind of activity can give a real advantage.
Despite the usefulness of specialization - it's simpler in theory than in real game. In most situations you will control some kind of hybrids, but knowledge how to focus cities on one function is very helpful.
There are three main kinds of specialisation - The Commerce City, The Production City and The Great People Factory.
The Commerce City - the main goal is to maximise commerce. Further it's possible to specialize into a research centre (emphasizes on science) or a financial centre (emphasizes on amount of income).
The Production City - your industrial centre, a place where you are able to quickly produce new units and raise expensive buildings (especially Wonders). Its main function is to build up your military and create some Wonders.
The Great People Factory - city focused on generating "Great People". It's possible to bias it on specific kind of GP. Moreover, due to big number of specialists it will generate a lot of science/commercial/cultural output - depends on sort of specialists.