This only makes sense if the photon exists, there is no classical analogue, because the energy of classical waves depends only on their amplitude, not frequency.
Proportionality factor in the Planck-Einstein relation between light energy and frequency.
Intuitively, the Planck constant determines at what length scale do quantum effects start to show up for a given energy scale. It is because the Plank constant is very small that we don't perceive quantum effects on everyday energy/length/time scales. On the , quantum mechanics disappears entirely.
A very direct way of thinking about it is to think about what would happen in a double-slit experiment. TODO think more clearly what happens there.
Appears in the Schrödinger equation.