This is a very famous topic and it is covered very well in the Wikipedia article on the photoelectric effect. In fact it is so famous I feel like maybe asking the question is some sort of joke. However, since you asked, …
The energy of the liberated electrons is independent of the intensity of the light. When discovered this curious fact was one among a handful of observations that indicated something was terribly wrong with our concept of the universe. No theory of light as a classical wave could explain it. To explain this impossible observation, in 1905 Einstein postulated that light energy must come in discrete bundles each with a fixed energy (photons). In 1921 Einstein was awarded the Nobel prize in physics for this idea rather than the theory of relativity for which he is now so well known. (Well, for all his contributions, but specifically for postulating quantized energy and photons to describe the photoelectric effect) As this was a seminal step in the construction of quantum mechanics it certainly worthy of a Nobel prize.
Pshkow F. Mahmood You might find it helpful to look at it this way. If the characteristic frequency of the electron is f1 then its energy is hf1. An incoming photon with frequency f2 will have energy hf2. The total energy of the electron after absorbing the photon is h(f1 + f2). If this energy is sufficient to cause an electron to leave the atom then it will do so.
Increasing the intensity with the same frequency of light just adds more photons and releases more electrons.
Increasing the frequency of the light will increase the kinetic energy of the escaping electron.