1. A black body is a hypothetical object that absorbs all incident EM radiation.
2. First, lets delve a bit in to what the classical wave-theory of light predicted. It predicted that the intensity of black body radiation (BBR) as wavelength got smaller would approach infinity (known as the UV catastrophe). However this was inconsistent with experimental results which showed that the intensity dropped to 0 at wavelengths around UV.
Now Planck resolved this by stating that the energy absorbed and released by black bodies are quantised. This meant that light was composed of packets of energy proportional to the frequency of it (E = hf). Planck hypothesised that for certain quantum changes to occur, certain packets of energy must be absorbed or released. I say "certain" because packets of higher amounts of energy must be absorbed for larger quantum changes, and smaller amounts of energy must be absorbed for smaller quantum changes in an "all-or-nothing" fashion (half or a quarter of a packet of energy cannot be absorbed).
After a change to a higher quantum state, it changes back to a lower quantum state, releasing a packet of energy.
Thus, we can see that the energy radiated by a black body is quantised.