Upvote:5
When a German official makes a decision and you do not like the outcome, you can go to court. German courts are organized into criminal, civil, administrative and some other branches.
An appeal makes sense if the official made an obvious, simple error or if you have lots of money to spend on lawyers. It probably makes no sense in your case, but they need to tell you anyway. Being told that and where one can appeal is completely routine on German official documents, and does not suggest that one should appeal in the specific case.
How to convince a German visa official that you will leave again: