Linked is the Wikipedia article to the German model, which is relatively short and will hopefully give you a better idea of how the Bismarck model functions.

And, furthermore, when people receive private insurance, the public system has to serve fewer people with the same amount of money (as those who opt for private insurance still pay the nominal fee for the public system), and so everyone gets better outcomes, in the private and public systems. Inequality is acceptable if it means that everyone’s situation improves.