Quantum mechanics initially interested me a decade or two ago because predictions are based on probability distributions and appear to be related to state-space modelling in fisheries stock assessment. However, it is very hard to find a comprehensive but simple explanation of quantum mechanics. Often, you get told you can't understand it without complex mathematics. This is foreign to me since I generally use mathematics to represent a hypothesis and test it by seeing how well it replicates observations. And the interpretations are just weird. For example, the many universe interpretation and the instantaneous collapse of the wave function after measurement appear irrational to anyone except a physicist. Even top physicist including Einstein and other Nobel laureates disagree which interpretation is correct with some laureates considering the interpretations are irrational. Sir Roger Penrose says collapse of the wave function is absolutely nonsense. To me, the only somewhat rational interpretation is related to the Pilot Wave interpretation, but were the pilot wave is created by the source of the particles. This leads to the Critical Mass Interpretation.
Two of the main weird concepts are:
Duality: Quantum elements act both as waves and particles. This is demonstrated in the double slit experiment where a single photon fired through one slit still produces a banded pattern (when this is repeated lots of times) as if waves are created at each slit and interfere with each other.
Entanglement: Two "particles" are related more than can be explained simply by being created with correlated characteristics. When they are measured in the same way they give the same (or opposite) result, but when the measurement type is chosen randomly the probability of being the same is too small. This implies that when one "particle" is measured, it changes how the other one is measured, but this is not possible.
Here I try to explain these concepts with as little math as possible.