Density functional theory (DFT), one of today's most popular methods of solid-state physics and quantum chemistry research, gives, in principle, an exact description of many-electron systems, relying on various density functions of 3 variables instead of the 4N-variable wavefunction (with N the number of electrons). However, in practice, mostly its single-particle Kohn-Sham approach is applied, which - though also exact in principle - gives up the original simplicity of the theory to some extent by introducing N single-particle orbitals. In my talk, I will show that the energies corresponding to the one-electron orbitals have significant direct physical meaning, giving certain many-electron excitation energies, provided the exchange-correlation potential possesses the necessary derivative discontinuities.