It simply means that electrons can only have certain energies. These "levels" are often in terms of n, such as n1, n2, n3, and so on. Let's say that n1=1000 eV (a unit for energy) and n2=2000 eV. It would be impossible for an electron in an atom to have any energy between those two values. This follows true for any energy level; this can be shown better like this: there can be no electron energy found between nx and nx+1 when the electron is in an atom.
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