City Connections are a feature of Polytopia that allows you to get bonus Population to your capital and the connected cities for forming them. You can create them in two ways, by land or by sea.
A city Connection is created when a city in your empire is connected, either by Roads or by Ports, and gives 1 Population to the capital city and to the other city.
Upon researching Roads, the Network task is unlocked, which awards the Grand Bazaar monument for connecting 5 cities to your capital (having 6 in total).
Roads
Building a contiguous line of Roads over land from a city to your capital (or from a city to an already-connected city) will complete a city connection. You may also form City Connections with Roads in neutral territory, but not in enemy territory. This is useful when you have a large landmass with cities to connect, however it cannot cross mountains nor can it extend over water.
Trade Routes
When a Port is placed, it immediately forms what is known as a Trade Route with any other owned Port within 4 tiles over water (not including the port tiles themselves). This also serves as a City Connection, connecting cities with an adjacent port. However, this requires the cities to be adjacent to the port. Luckily, you can build Roads to ports to complete the City Connection.
Breaking Connections
It is possible to Break a city connection. For example, if you are connecting the city via ports, you can Destroy them and disconnect the city. This will remove the 1 population given to both cities when connected, and may result in producing Anti-Food. It can also be done if an enemy captures a city that either is connecting a third city to your capital, or the capital itself, all affected cities will become disconnected.