It's common for different teams to work on different services but often there is cross-teams contributions. A Run Book is a template to hold all critical information about a service needed to understand how the service operates.
The authors of the template also state that:
but remember: discussion, not documentation is where the value lives in Run Book collaboration
In that sense, a Run Book will be a great place to hold all technical information about a service and seek input from other people.
Read more here.