If you are not a EU or EEA citizen, you usually need a residence permit (Aufenthaltstitel or Aufenthaltserlaubnis) to live in Germany. You apply for a residence permit at the Ausländerbehörde, or at the German embassy or consulate in your home country.
There are different residence permits for different purposes: working, studying, starting a business and more. The Blue Card, the work visa, the student visa and the freelance visa are residence permits.
The residence permit is a plastic card.