In the photon model, when light illuminates a metal surface, individual photons are absorbed by individual electrons. The electron will gain all of the photon's energy at once, and it will be ejected from the surface if this energy exceeds the work function of the metal.
A monochromatic light source produces only one frequency, f, of light, meaning all the photons will carry the same energy. This leads to a threshold frequency, f0, where the energy carried by each of the photons is equal to the work function. Below this frequency, none of the photons have enough energy to release an electron, so we see no photoemission.