The "Green Card" is your proof of insurance for international road transport. It contains important data about the vehicle, its owner and its insurance. It is available free of charge from the car insurer.
The handling of a claim is made much easier by the Green Card, so it is best to keep it handy in the glove compartment of the car at all times.
By the way: In the case of accidents abroad, the national law of the country in which the accident occurs generally applies. The legal minimum coverage is often much lower than in Germany. The result: the compensation is considerably lower.