If you are an employee, and you make under 66,600€ per year, you are compulsorily insured (Pflichtversichert). This means that public health insurance companies must accept you, even if you are very sick. It also means that you can't have private health insurance.
When you are not Pflichtversichert, you are voluntarily insured (freiwillig versichert). Public health insurers do not have to accept voluntarily insured people. Students and freelancers are freiwillig versichert.