The Fe-57 nuclear magnetic resonance (NMR) shielding and chemical shift in ferrocene, Fe(C5H5)(2), are studied using density functional theory (DFT) and gauge-including atomic orbitals (GIAO). Electronic factors contributing to the chemical shift are discussed in detail. It is shown that the chemical shift is entirely determined by paramagnetic contributions which in turn are dominated by metal based occupied-virtual d-->d couplings. In particular, the HOMO-1(a(1)') and the HOMO (e(2)') couple with the LUMO (e(1)"). It is argued that the Fe-57 nucleus in ferrocene is less shielded than in the reference compound (iron pentacarbonyl) due to a smaller HOMO-LUMO gap, resulting in stronger interactions between occupied and virtual orbitals. The influence of the XC functional on the calculated molecular orbital (MO) energies of frontier orbitals is discussed. Different generalized gradient approximations (GGA) give similar results whereas hybrid functionals that incorporate part of the Hartree-Fock exchange stabilize occupied MOs strongly and destabilize virtual MOs. HOMO-LUMO gaps are nearly doubled as a result. The previously noted "dramatic influence" of different exchange-correlation (XC) functionals on the calculated chemical shifts is analyzed. The influence of the XC functional is realized through the paramagnetic part of the shielding; hybrid functionals increase it in absolute terms as compared to pure DFT (GGA). It is argued that three factors are responsible. These are (i) the increased occupied-virtual gaps, (ii) the more diffuse nature of virtual orbitals, and (iii) the coupling due to the Hartree-Fock exchange in hybrid functionals. The last two factors increase the paramagnetic part of the shielding, and this effect is only partly reversed by the increased occupied-virtual gaps that result in reduced interactions. It is suggested that new model XC functionals for the calculation of NMR shieldings should be developed aiming at both, accurate energetics and a correct representation of the XC potential. The wealth of precise experimental NMR data could be used as input for this purpose.