Germany has a national health insurance system. In spite of this, health insurance in Germany is not automatic. Instead, at the beginning of your stay, you must arrange to get health insurance coverage. This is a legal requirement.
Since the application process usually takes at least two weeks, you must ensure that you have temporary (for example travel) health insurance for at least the first month of your stay in Germany.
How you obtain health insurance depends upon your employment status. If you have an employment contract (called TVöD in German) then you are an employee and one set of rules apply. If you have a stipend (called a Stipendium in German) then you are not an employee, and a different set of rules apply.