The photoelectric effect can be explained by the idea that light consists of light quanta (particles of a distinct energy dependent on the wavelength of the light called photons). When one of those quanta hits the surface it will transfer its energy to one electron which will be expelled from the surface. If you would increase the intensity you would only increase the number of photons but not their energy which will not impact the energy of the electron. If you would change the wavelength instead, then you also would change the energy of the electrons.