In quantum mechanics, what does the commutation and non commutation between operators representing mechanical quantities mean? What is their physical meaning?

In quantum mechanics, what does the commutation and non commutation between operators representing mechanical quantities mean? What is their physical meaning?

This question can be exchanged, not answered. Let me talk about my understanding. The commutation of mechanical quantities shows that two physical quantities can be accurately measured at the same time, that is, two physical quantities can take eigenvalues in the same representation at the same time; on the contrary, the commutation shows that two physical quantities cannot be accurately measured at the same time, that is, they cannot take eigenvalues in the same representation