How does a nucleus function like a mayor?

If we were to think of a cell as a city, we can think of various organelles as components of the city. In such a scenario, we can think of the cell's nucleus as the mayor of the city. A nucleus controls all the activities of the cell and can be thought of as the boss of the cell (since it regulates all the activities). Similarly, a mayor of a city controls all the activities of the city and regulates them, as and when needed. The nucleus uses DNA (deoxyribonucleic acid), which houses genetic information, to direct the protein synthesis and thus control cell's activities. Similarly, the mayor uses the city's blueprint to help him decide on what needs to be done.  

We can also think of other roles for cell's organelle; cell membrane can be thought of as the city limits or borders, ribosomes can be thought of as workers, DNA can be thought of as the city's blueprints, etc.

Hope this helps.