A dotted line manager is a supervisory figure who can assign tasks to employees, has some form of authority over employees but who is not their direct, or straight line, manager. Dotted line managers are a fixture of multi-level management systems in which employees are answerable to multiple people within a larger hierarchy of managers.
A straight line manager is an employee's direct assessor and superior. They are most often responsible for reporting on the employee's performance and for handling such procedures as firings, raises and promotions. They are directly involved in the day-to-day work of their employees in a way dotted line managers are not.
Dotted line managers have a much looser form of authority and interaction with their employees. Their department may abut the one in which their employees work, making it necessary for them to be able to issue instructions but leaving them out of the performance review and assessment pipeline for those specific people.
Dotted line managers can be a helpful presence in heavily specialized workplaces where a single person may perform multiple special duties within a corporate structure. They can increase the overall competence of management's interaction with that person and help them remain on task without micromanaging.