Indeed its as Bryan said.
The user who creates a dashboard is the only one who has full admin rights. That user is the only one who can modify the dashboard.
That is also the only user who can share that dashboard with other users. Those other users can only see the dashboard. If those others users want to edit the dashboard, they will need to clone the dashboard so that they get there own copy of it.
The user who created the dashboard can also change the owner of the dashboard. That way a other user can get admin permissions to that dashboard.