The photoelectric effect was the experiment in which light rays that shone on an experimental apparatus caused electrons to be emitted. Photons of light of different frequencies causes the device to spit out electrons of different energy. In particular, the energy in a photon is equal to its frequency times a constant (Planck's Constant). So a photon with a high frequency is more energetic than a photon with lower frequency. This energy equals the energy of the electron emitted plus the amount of energy it took to emit the electron.

As equations, the energy of a photon is E=hf, where E is the enrgy, h is Planck's Constant, and f is the frequency. When the energy of the emitted electron is: K=hf-W, where K is the kinetic energy of the electron and W is the "work function" of the material emitting electrons. The work function is the minimal amount of energy necessary to kick an electron out of the material the light is falling onto.

Here's where it proves the quantization of energy: the work function is a set amount of energy. Below this energy, no electrons get kicked out of the material. The photons have to have some minimal frequency for the device to emit electrons. Basically, they have to have a minimal quantity of energy for the effect to work. Any excess energy over this amount goes into speeding up the electron; it increases the kinetic energy of the electron.