Each orbit or shell of an atom has a certain energy state associated with it. These energy states are the only energies electrons can have in an atom, hence their energies are quantized.
The concept of the energy in an atom being quantized rather than continuous is apparent when looking at emission and absorption spectra of atoms. Electrons can only exist at certain energy levels, so when an electron gains or loses energy, there are specific photon energies associated with the energy changes. These energies determine the colors seen in an atom's emission spectrum and the colors not seen in its absorption spectrum.