I spent some time this weekend, listening to about five of the Perimeter Institute's recorded lectures on the Foundations and Interpretation of Quantum Theory, available here. It was heavy going and I'm not sure I've learned a lot.
Let me just mention the problem. Quantum mechanics has an impeccable mathematical formalism, and a simple mathematical rule to relate what you calculate using the machinery with the outcomes of measurements. If you're satisfied with this then you belong to the "Shut Up and Calculate" school of physicists. What the formalism has trouble with is relating the mathematical formalism to our ordinary intuitions of the world. It is difficult even to explain how the illusion of what we perceive arises.
At this point, I refer you to Wiki.
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