The quantization of the energy of an electron inside an atom explains much of the behavior of atoms such as why atoms emit only discrete frequencies of light. An electron that is in a low orbit of an atom can absorb a photon causing the electron to jump to a higher orbit. The electron then emits a photon jumping back to the lower orbit.
The quantization of space-time is based on several natural units proposed by Max Planck that are based on five universal physical constants: Gravitational constant, Reduced Planck constant, Speed of light in a vacuum, Coulomb constant, and Boltzmann's constant
While most of them have no physical significance two of them Planck Length and Planck Time are the smallest possible measurements of space-time according our current understanding of the laws of Physics because of the uncertainty principle when a plied to these scales. This suggests that time and space themselves are Quantized.
Planck Length is the smallest measurement of length that has any meaning with in the laws of physics as we understand them today and Planck Length is about 1.616 252 × 10−35 m.
Planck Time is the amount of time it takes a photon to cross a Planck Length. It is the smallest measurement of time that has any meaning with in the laws of physics as we understand them today and Planck Time is about 5.391 24 × 10−44 s,
Quantization requires physical quantities like position, energy and momentum to have discrete values explaining much of what goes on in side atom and based on our current understanding of the laws of physics it suggest that time and space are quantized.