If you ask mayors and people who work with them to describe their jobs, you get a pretty long list. I spent several months doing exactly this - and here's what I learned. It's the closest thing that I've seen to a job description for Canadian mayors.
Mayors are expected to lead within three specific roles. Each of these are rather different from one another; and, they require different kinds of resources.
1. Mayors are Political Leaders - mayors are expected to lead their elected council, work with elected officials at other levels, and sometimes lead within a local political party.
2. Mayors are Executive Leaders - Canadian mayors are expected to play some role in the delivery of government services. This can involve very explicit roles in areas such as emergency management, or less explicit roles such as having a unique relationship with municipal staff and the administration of a variety of other organizations such as local boards.
3. Mayors are Community Leaders - this is the most difficult role, but mayors are expected to lead the broad and diverse array of individuals, groups and organization in their community.
You can read more about these roles here (check out Chapter 7).
Here's the important part: in practice, mayors tend to gravitate to one or more of these roles more than others. Sometimes it's based on the individual's skills or experience; other times, it's due to the particular circumstances. Importantly, when mayors don't lead in these areas, it shifts the dynamics of governance in their community. For example, in a city where the mayor focuses on community leadership but is not as effective as a political leader, we can expect to see other members of council stepping into that political leadership role (building coalitions on council, setting a shared agenda, etc). These patterns are fascinating - and will be subject to more research ahead.