The quantization of energy refers to the fact that at subatomic levels, energy is best thought of as occuring in discreet "packets" called photons. Like paper money, photons come in different denominations.
You can, for example, purchase items with a one dollar bill or a five dollar bill, but there are no three dollar bills. Money, therefore, is quantized; it only comes in discreet amounts.
In quatum physics, photons are packages of energy and correspond to differnt colors in the spectrum or different types of electromagnetic radiation (radio waves, microwaves, X -rays, etc).
A red photon has specific enegry value different from a blue photon. The red and blue photons are therefore "quantized" just as dollar bill denominations are "quantized". Each photon contains a unique amount of discreet energy.
More technically, the uniqueness -- or "quantization" -- of enregy is related to Plank's constant, which specifies "how quantized" energy can get.
The formula is: #E=hf# where #E# is energy, #f# is frequency and #h# is a very tiny constant called the Plank's constant (#6.62 * 10^-36 (m^2kg)/sec#). This constant regulates and "quantizes" the energy of the universe.