In order to get enroled at a German
university you will have to proove sufficient health insurance. More
info about it can be found here .
For students who are cititzens of the European Union this is easily done by use of their European health insurance card (EHIC). For your enrolment as an exchange student we just need a copy of the card which should be valid for the whole time of your stay.
In case you don't have a EHIC, but brought private health insurance from your home country which is also valid in Germany you could obtain a waiver for the health insurance requirement (the "Befreiung von der Versicherungspflicht") from one the German statutory health insurance companies. The "Befreiung" will then suffice for your enrolment. But please keep in mind that for the whole time of your studies in Germany you won't be able to get into the statutory health insurance system.
If you don't have any health insurance at all you either have to get statutory health insurance or private health insurance (and then the "Befreiung") in Germany. Please keep in mind the health insurance information from the Immigration Office  when obtaining your health insurance. If you get statutory health insurance we will need the confirmation form (three pages).
Statuory Health Insurance offices close by:
AOK  Barmer  Techniker Krankenkasse