A more thorough explanation:

Mayorship

Mayorship refers to the position or role of a mayor. It is the term used to describe the status of being a mayor.

John Smith was elected to the mayorship of his town last year.

The mayorship of New York City is a highly coveted position.

These examples illustrate how the term mayorship is used to describe the position of being a mayor. In the first example, John Smith is referred to as holding the mayorship of his town, indicating that he is the current mayor. In the second example, the mayorship of New York City is described as a highly coveted position, emphasizing the importance and prestige associated with being the mayor of such a large and influential city.