The statutory health insurance belongs to the mandatory insurances and covers medical costs and check ups. In addition, it takes care of other costs that are health related. In case the illness lasts longer than 6 weeks, the health insurance takes over your salary by paying you a salary replacement benefit.
If you are self employed, you can either insure yourself statutory or by means of a private heath insurer.
In case you would like to be using a private heath insurance, be advised, that there are tremendous differences. Do inform yourself extensively about the scope of services and how high the monthly premiums are. In the end, comparing offers will be your personal gain and may save a lot of money.