What makes someone deserving of a Ph.D.? Few days back while attending a thesis defense, one Professor was asking the defender why does he think, he deserves the degree. I was wondering since then, is there really any general answer for that? or the answer should be given describing my own work and then emphasis them how it is important for research field?

I asked the question here to know your opinion about it and to list down what could be the possible answers to this question.
For a Ph.D., my favorite explanation is this cartoon by Matt Might.

In short: a Ph.D. is a measurable contribution to a sum of human knowledge.

To be able to answer this question, all you need is an idea of how to describe what you have discovered, and how it fits into the context of work by others that has come before.  This is often not easy to answer, but an important thing to think about as one is writing one's thesis in any case.