This feature is used to destroy your city so that it can be rebuilt elsewhere or you can leave the game. Abandoning destroys all buildings, including level tens, and kills all troops in your city. Use with caution. Once you have abandoned a city you cannot get it back without having to rebuild it completely. You can not abandon your city if it is the only one you have.
How to Abandon a City
In the Castle window there is a button saying "Abandon City." When this is clicked on you will get a message asking if you are sure you want to abandon the city. If you click that you are then your city will disappear from the domain.
Uses of Abandoning a City
People who are leaving the game often abandon their cities to get their might to drop and kill their troops. This makes them a smaller target for farmers.Another use is as a "free" Portal of Order, the city is moved from one place to another. However, when used like this it is necessary to rebuild the city from scratch which makes it less useful. Abandoning your cities cannot get you off of the domain because you cannot abandon your last city.