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. I know the interpretation before I know the mathematics.
Quantum mechanics is weird and even the top physicist including Einstein and other Nobel laureates can't agree on an 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.