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Basically, in the photoelectric effect, light is not acting like a classical wave, where the bigger or more intense the wave is, the more energy it has. So increasing the intensity of light does not add to the energy of photons. Rather the energy of a photon is proportional to its frequency, so even a low intensity light can eject electrons if it has high enough frequency, meaning that the energy of the photons are high enough to remove these electrons from their surface. Therefore, if the energy of the photon is not greater than or equal to the energy required to move an electron, then electrons will not be emitted even for high intensity light, as the key to removing electrons is energy here, not intensity.
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