Most Germans keep their professional and private lives separate. An invitation to a German home therefore indicates that they regard you as a potential friend and would like to socialize with you more often.

If you can’t accept the invitation because of other commitments, do not hesitate to say so, but do thank your hosts for the offer. However, if you choose to accept, you should take care to cancel the appointment only in case of unavoidable emergencies. As Germans indeed like punctuality, you should arrive on time, albeit not too early.

(If you are early, you might interrupt your host’s preparations.) If you are more than 15 minutes late, you should phone them on the way in order to apologize. (Germany - Language, Culture, Customs and Business Etiquette, 2016)