How to understand the wave-particle duality of quantum mechanics?

Question

As the theory shows, quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems.

Here, I have a question: how to understand how the wave-particle duality of quantum mechanics relates to nature, the real physical world of, say, a photon, or an electron?  

"Never in the history of science has there been a theory which has had such a profound impact on human thinking as quantum mechanics; nor has there been a theory which scored such spectacular successes in the prediction of such an enormous variety of phenomena (atomic physics, solid state physics, chemistry, etc.). Furthermore, for all that is known today, quantum mechanics is the only consistent theory of elementary processes. "--Max Jammer： The Philosophy of Quantum Mechanics: The Interpretations of QM in historical perspective.  John Wiley and Sons 1974.

"Scientists have been using quantum theory for almost a century now, but embarrassingly they still don't know what it means.  An informal poll taken at a 2011 conference on Quantum Physics and the Nature of Reality showed that there’s still no consensus on what quantum theory says about reality — the participants remained deeply divided about how the theory should be interpreted"--https://www.quantamagazine.org/how-to-tame-quantum-weirdness-20170216/

“Debates in the foundations of quantum mechanics sometimes appearas endless parti-
san squabbling between dogmatically-committed proponents of different viewpoints,
none of whose minds are ever changed. Still, in addition to learning how proponents
of different theories describe and develop their favored perspectives, it can be valu-
able to understand the criticisms that proponents of one theory level against its rivals.”
--Travis Norsen: Foundations of Quantum Mechanics | An Exploration of the Physical Meaning of Quantum Theory   http://www.springer.com/series/8917

"My own conclusion (not universally shared) is that today there is no interpretation of quantum mechanics that does not have serious flaws, and that we ought to take seriously the possibility of finding some more satisfactory other theory, to which quantum mechanics is merely a good approximation. "--Weinberg Steven,  Lectures on quantum mechanics /  ISBN 978-1-107-02872-2   http://www.cambridge.org/9781107028722

Comments

The quotes have nothing to do with your question. They are about unsolved problems in the foundations of quantum mechanics, not about wave-particle duality.

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A moving wave packet is not you favorite understanding?

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Maybe the answer here will help you ,