Work function is the minimum energy required to set off the photo-electric emission. As the incident radiation falls on electrons they absorb defined wavelengths and if they gain enough energy they jump out of metal. But the energy absorption depends is very specific and depends on the initial energy level of electrons. Since all electrons are not in same energy level, all of them can’t absorb the monochromatic wavelength. Since different electrons start from different energy levels so there a energy distribution of photo-electrons.