If we have a function of quantity to have a Poisson math relationship with Hamiltonian, which is kinetic energy + potential energy, {Q, H}, and the change of Q per time t can be computed as follows

Knowing the key here is highlighted in red, dx/dt, dp/dt is known physical characteristics(Newton’s), then mathematically dQ/dt = Poisson bracket of Q and H. So if dQ/dt = 0, i.e. Q is conserved along time, then the Poisson bracket Q and H = 0, we say this quantity or function Q Poisson commute with H.