What is Potential energy?

To every conservative force one attaches a potential energy $E_p$, a number depending on position alone, defined by $W_{AB} = E_p(A) - E_p(B)$: work delivered is potential energy spent. Fixing $E_p = 0$ at a chosen reference point fixes it everywhere; the choice shifts all values by a constant that cancels from every difference. For the weight this gives back last year’s $E_p = mgz$, now valid along any path. Friction can own no $E_p$: a route-dependent bill is no difference of endpoint numbers — only conservative forces store retrievably, exactly what the name conserves.