Light can be modelled as photons - discrete quanta of light that carry fixed quantities of energy.
The energy of a photon with frequency
The photoelectric effect occurs when light is incident on the surface of a metal. It is a one-to-one interaction between photons and electrons on the metal, and electrons can be emitted as photoelectrons.
The intensity of light does not cause higher energy electrons (energy doesn't accumulate), instead intensity is proportional to the number of electrons emitted.
The energy of the emitted electrons depends on the frequency of the light. The frequency must be above the threshold frequency for electrons to be emitted. The corresponding energy, the work function, is the amount of energy needed to liberate electrons from the surface of the metal.
Every path from an emitter to detector can be represented by a phasor. For most paths, the phasors curl up and cancel out, producing a small or zero resultant. The intensity is proportional to the square of the length of the resultant phasor.