depending on your age the Jobcenter will give you - and you have the right to get - some kind of activation offer after some period of unemployment, where you have received dagpenge.
If you are under 30 years old, this offer will given within the first 13 weeks of unemployment.
You are obliged to accept the offer (and you have the right to get the offer).
An activation/employment offer may consist of business practice/internship, job with public financing/support, courses or education.
Regarding the internship: It is a short-term internship of up to 4 weeks at either a private or public company.
However, if you are an unemployed graduate with a higher education, you can participate in business practice/internship for up to 8 weeks. It is a condition that you have not had regular employment after your education is completed. And its only possible if you receive unemployment benefit.
If you know a company or public employer, where you think you can have an agreement with internship, then you have the option to decide your self, where to have your internship. But if you dont find a place your self, then the Jobcenter may find something for you (that you must accept).
Normally there will not be so many requirements about what kind of internship, and in what company etc., but overall the Jobcenter accepts something that may give you better chance to have a real job afterwards.
Hope this helps, otherwise you can make a comment here.