Its all about photons have energy E = hf . In simple terms the colour of light determines the amount of energy E. E cannot be increased if the light is more intense or is of greater power but can only increase by increasing its frequency i.e more towards the violet end of the visible spectrum
When light of frequency f, cannot emit photoelectrons even higher intensity will give the same result. Hence quantum theory of light puts forward the idea that the photon E remains the same but only the rate of photon arriving increase when intensity is increased. The photon energy E is still less than the work function of the metal.
When light of frequency above the threshold frequency is incident on the metal, even very low intensity light can produce photoelectric current. The photon energy E remain the same when intensity is low, photon energy minus the work function result in excess energy in the form of kinetic energy of photoelectron. Increasing the intensity will result in greater photocurrent as the rate of incoming photons of energy E increase but not the kinetic energy of the photoelectron since photon energy remain the same .
All the above in based on the quantum theory that helps us to see light as packets of energy where colour and intensity is seen in a new way(particulate nature) as compared to the old way (wave nature)
An example of wave nature is intensity depends on square of amplitude which imply that intensity increases the energy of the wave.Wave energy arrives with time . If exposed to light for a longer time will receive large energy. Energy is power x time . None of these is able to explain the photoelectric effect.