Einstein contributed greatly to both quantum theory and black body radiation. Although Max Planck first discussed the idea of the radiation emitted by a black body being quantised, i.e. radiated in packets rather than continuous waves, it was Einstein's use of Planck's hypothesis to explain the mysterious photoelectric effect that really kick-started quantum physics. He explained that when light of a certain frequency above the threshold frequency for a metal was shone on that metal, it caused electrons to gain energy and 'jump' into the conduction band, and their movement constituted a flow of current when a potential difference was applied across the metal. The ingenuity in Einstein's explanation was that the energy received by the electrons was quantised, i.e. that the incident radiation was not a continuous wave but made up of small packets or particles, called quanta, each with an energy given by Planck's equation E=hf. The electrons accepted the energy from radiation in whole integral multiples of quanta - the 'all or nothing' principle where if the energy provided by the quanta of light was greater than the work function of that metal, the electron would gain this energy - otherwise it would gain nothing. Mathematically, K.E. = hf - W . Where W is the work function and K.E. is the kinetic energy of the electrons. Thus the kinetic energy of the electrons was quantised, and this explained the photoelectric effect where the kinetic energy of the electrons was enhanced by increasing the frequency of the incident radiation, and not the radiation intensity as would be expected in classical physics.
Thus Einstein contributes greatly to quantum theory by using the particular nature of light, and the idea of quanta first formulated by Max Planck, to further quantum physics into a new era where every wave had particle nature, and all electromagnetic radiation was quantised (not just those emanating from a Black Body). Finally in terms of his contribution to Black Body Radiation, it was Einstein's explanation of the other phenemonen that lended credence to Planck's mathematical approach to solving the problem of the black body curve. In this way rather than contributing directly, Einstein in fact provided support for Planck's hypothesis.
Somewhat of a quick dodgy brothers job but its all I can think of atm
