Does your supervisor have to be able to understand your thesis? I am currently writing my master thesis in mathematics and for those who are more familiar with the subject, I am more into analysis whereas my supervisor is more into computational sciences. My project is on an application of analysis and there is also a numerical component.

I will soon submit my first draft to my supervisor but I am slightly anxious about how he will react. 

To describe it quite generally: my background is very much in the theory of mathematics and I am a relative novice in the computational sciences, thus I am treating that component as an end-goal of my thesis while building up to it rigorously with the theory that I have become acquainted with over the years. Incidentally, in our meetings, my supervisor focuses most of his attention on the "results" of my thesis rather than the technicalities in between.

You could argue that there is a "mismatch" in some sense. However, I am very much interested in this application which my supervisor does, but I would like to do it in my own style. This brings me to my question: do I have to write my thesis in such a way that he is able to read it, or is it quite common for them to seek the assistance of other professors who are better acquainted with the theory?
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?