Inside of a vacuum tube you place two electrodes and measure the current with an extremely sensitive ampere-metre. Photons of the light which hit the cathode will excite electrons causing them to leave the cathode and thereby creating a current.
With increased light intensity the current will also increase, so far nothing special. Now you can also vary the energy an electron must have in order to leave the cathode. One can do this by applying an electrical field to the electrodes. What you can observe than is from a classical point of view not explainable: From a certain voltage on you can not measure a current anymore, i.e. no electron has enough energy to leave the cathode. This voltage depends on the wave length of the light, only.
Treating light as a wave this observation can not be expected. An oscillating wave will cause the electrons to oscillate and thereby receiving kinetic energy (which eventually causes them to leave the cathode). After increasing the light intensity the necessary energy should eventually be reached. But as observed that is not the case.
The reason is that light has both properties of a wave as well as properties of a particle (wave-particle dualism). Einstein gave an explanation for the observation which is the foundation of the quantum theory. For this explanation Einstein was awarded with the Nobel price in physics.