The registration certificate part 2 (Zulassungsbescheinigung Teil 2) contains detailed information about the car and who’s name the car is currently registered under and the name of the person it was registered under previously.
Unlike the registration certificate part 1, you’re not obliged to keep the certificate with you at all times. In fact, it’s better to keep it safely at home. You only have to bring both certificates when you register or sell your vehicle. This is to prevent stolen vehicles from being driven or sold.
Please note: The registration certificate part 2 is not an official certificate of ownership although it can be used an indication in the court of law in case there is a debate on ownership.