Similar to how approvals work for time off requests, managers by default have the ability to create and edit goals for employees who are their direct reports. This default setting can be changed under Company Settings > Roles and Permissions > Manager Role.
Only users with the ability to "View and edit" a goal for an employee can create goals for that employee and update progress on any of their goals.
Employees can always view, create, and edit all of their own goals. This setting cannot be changed, but managers are be notified when any changes are made to an employee's goals through daily digest emails.
Custom roles can be given this permission as well, and Super Admins have "View and edit" access to all employees by default.