The energy of a photon depends on the frequency: $E=h \nu$. This is not a classical result.
So classically: To extract electrons from a material you need a minimal energy. This can be provided by a minimal intensity.
But: from a quantum mechanical point of view this reasoning breaks down. That's the discovery of the photoelectric effect (and its correct explanation): to extract an electron you need a minimal energy that can be provided by photons above a frequency (and thus energy) threshold.
If the energy of the incident photon is higher than the "extraction work" of the material (the energy needed to extract the electron) this additional energy is transformed in kinetic energy of the [free] electron.
Therefore an increase in the intensity of light whose frequency is bellow the threshold cannot help as in the classical case.
Increasing the intensity of the light means a higher number of photon (thus more total power but I does not mean more energy per photon), this can allow to extract more electrons ("one by one").