We have investigated the electronic structure and the Fermi surface of SnO using density functional theory (DFT) calculations within recently proposed exchange-correlation potential (PBE+mBJ) at ambient conditions and high pressures up to 19.3 GPa where superconductivity was observed. It was found that the Sn valence states 5s, 5p, and 5d are strongly hybridized with the O 2p-states, and that our DFT-calculations are in good agreement with O K-edge X-ray spectroscopy measurements for both occupied and empty states. It was demonstrated that the metallic states appearing under pressure in the semiconducting gap stem due to the transformation of the weakly hybridized O 2p-Sn 5sp subband corresponding to the lowest valence state of Sn in SnO. We discuss the nature of the electronic states involved in chemical bonding and formation of the hole and electron pockets with nesting as a possible way to superconductivity.