This is simply explained by the photon model of light. In
that model an electromagnetic wave carries its energy not like a continuum, but
as multitude of grains of energy which have the same individisible amount of
energy. The indivisible grain of light energy, also called "light
dart" by Einstein, and then electromagnetic energy quanta or photons is
given by the Planck-Einstein's law:
Ephoton =h⋅f
where f is the frequency of light. For each single
photon at the same frequency.
From the point of view of photons, a more intense light is
not made of "higher waves", but of a higher number of photons.
Than is obvious that, if each photon is capable to expel an
electron, the more intense is the light the more number of electrons will be
expelled. If frequency is under the threshold, then even the higher intense
light will be equally incapable to eject even a single electron.