Sounds to me like you're taking about one of two possible things ... abandoning a city, and relocating your Capital.
To abandon a city, either ...
- Have the city at size 1 and not growing while building a Worker. On the turn that the Worker would otherwise be complete, you'll get a dialog box. Choose to 'abandon' the city, and it'll disappear, leaving a Worker behind.
- Have the city at size 2 and not growing while building a Settler. Same as above, at the beginning of the turn that the Settler would otherwise be built, you'll get the same dialog box. Abandon the city, and it'll leave a Settle behind.
The second of the above two can be used to relocate your capital to a better position, often for anti corruption purposes.
When you choose to abandon your capital, the game will automatically move your capital to another city. This saves the 1000 (?) shields required to rebuild the Palace elsewhere.
Which is nice.
