Indeed, Einstein made use of Planck's constant in his explanation of the photoelectric effect. If the production of a photoelectron is caused by the complete absorption of one photon of energy hn, then the maximum kinetic energy, K, that can be observed for such an exiting electron is K = hn-f, where f is the workfunction (electron binding energy) of the material that the electron comes out of. This completely explained the experimental results for the photoelectron energies. It also gave credence to the idea of light intensity (or brightness) as only changing the number of photons (and hence photoelectrons), without altering their kinetic energies.

The "generic" name given to one of these packets is "quantum" (quanta for plural). Now, the theory of quantum physics was born - from the basic nature of light. Of course, we did not really explain how a photon has Maxwell-type fields "inside" it, or how quanta can act as if they were waves. So our story of light is not close to being done yet, but we will press on.