the simple answer to your post's question is efficiency. If you do things more efficiently in this game, you win, plain and simple.
You can build 2 cities to produce 50 commerce (which you then use for research, money, espionage, whatever). Or you can build 1 city that produces the same 50 commerce.
The civilization that only needs 1 city to get it done is doing better because it is paying less in city maintenance and civics costs, and it only took 1 settler and X number of workers to get it going, vs. what it would take for 2 cities. So compound this over the span of many cities and you see how it adds up.
As was said above, it takes hammers to build everything. So if you have a lot of cities you might need a lot of courthouses or libraries or whatever to make each city "productive." But if you can get fewer cities pulling more of the weight, everything is more efficient. You only need to build 1 library in a city producing 500 beakers, and that library gives you 25% bonus to all those beakers. Yet it was just 1 city, so all you needed was 1 library, 1 courthouse, etc!
The same thing goes for working city tiles... if you build a cottage and keep working it to develop into a town eventually, it will produce a lot more commerce more efficiently than building a lot of cottages and needing more population to work all of them.
Conversely, smart expansion is important to an extent because it denies land to your opponents and gives you access to more special resources. But people have proven in their games that you don't need to fill half the map with your cities to build up a huge army to crush everyone else, or build a spaceship, or get a cultural victory.
