Today I got letter from the editor of a journal saying that the reviewer found my work interesting but there are some points which he wants me to clarify. Now, one of the points he made is that he doesn't understand how I got from equation x to equation y and he wants to clarify how. Does that mean that I need to explain this in the paper itself or in the document that is send along the revised version, which explains my respond to the reviewer and what I have changed in the revised version?
It doesn't matter what the reviewer wants - you need to do what's best for your paper.
... which is to clarify things in the paper itself.
Think about it: a reader of your paper - one who was trying hard to understand it -was not able to understand your paper, or at least was unsure enough about it that it was worth mentioning. Since they are a reviewer you have a chance to explain things privately to them, but that's not going to be the case for most of your other readers. Some of them are going to hit the same roadblock, but instead of contacting you, they're just going to toss your paper aside. At best you lose a possible citation, worse, they could come away with a low opinion of your rigor and of you as a researcher.
Remember that the paper will need to speak for itself, without the additional comments to reviewers. If one person found the paper confusing, then others are likely to as well.