>>12492092Quantum world is a probabilistic world. You model positions, states, energy or any properties of particles as probability distributions.
Imagine you sum enough of those distributions, for example by having a lot of particles inside "matter". There are mathematical asymptotic theorems that basically say you'll observe a coherent blob around a certain point. This blob is the "stability" you observe on a macro scale.
The idea is that even if, on the micro scale, you have uncertainties, on the macro scale, these uncertainties average out and form coherent stable structures.
This statistical approach to physics is the one used in Fluid Dynamics. Eg, you model molecules' movement inside gas as random (brownian motion), but the gas itself doesn't move randomly. I just assume that something similar happen on the atomic scale.
Not a physicist so probably the real explanation is more subtle.