Does your supervisor have to be able to understand your thesis?
YES most definitely. Obviously, if you supervisor cannot comprehend your project, they cannot supervise it.

This should only very rarely occur. I can only think of a situation in which the student has, from prior qualifications, superior knowledge about certain aspects of the project than their supervisor. In this case, perhaps supervision in the traditional sense is not really necessary, but merely some guidance and feedback.

In any case, if you want to publish your research in the field of your supervisor, then you should speak a language and use conventions that people like your supervisor can comprehend. If you cannot express your project in such a way, then how can you hope that anybody relevant can understand it?